2sin (example 3.3)

Time bar (total: 12.0s)

start0.0ms (0%)

Memory
0.1MiB live, 0.1MiB allocated

analyze47.0ms (0.4%)

Memory
-4.2MiB live, 92.1MiB allocated
Algorithm
search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%50.6%49.4%0%0%0%0
0%0%50.6%49.4%0%0%0%1
0%0%50.6%49.4%0%0%0%2
0%0%25.3%49.4%0%25.3%0%3
0%0%25.3%49.4%0%25.3%0%4
0%0%19%49.4%0%31.6%0%5
0%0%15.8%49.4%0%34.8%0%6
0%0%11.1%49.4%0%39.5%0%7
0%0%8.7%49.4%0%41.9%0%8
0%0%5.9%49.4%0%44.6%0%9
0%0%4.5%49.4%0%46%0%10
0%0%3.1%49.4%0%47.5%0%11
0%0%2.7%49.4%0%47.9%0%12
Compiler

Compiled 27 to 19 computations (29.6% saved)

sample6.5s (54.4%)

Memory
-224.9MiB live, 6 355.6MiB allocated
Samples
3.8s26 027×0invalid
634.0ms5 427×0valid
429.0ms2 829×1valid
Precisions
Click to see histograms. Total time spent on operations: 3.6s
const: 708.0ms (19.4% of total)
ival-sin: 660.0ms (18.1% of total)
ival-fabs: 524.0ms (14.4% of total)
ival-<=: 433.0ms (11.9% of total)
ival-sub: 322.0ms (8.8% of total)
ival-mult: 287.0ms (7.9% of total)
ival-<: 269.0ms (7.4% of total)
ival-add: 201.0ms (5.5% of total)
ival-and: 104.0ms (2.9% of total)
adjust: 70.0ms (1.9% of total)
exact: 50.0ms (1.4% of total)
ival-assert: 16.0ms (0.4% of total)
Bogosity

explain87.0ms (0.7%)

Memory
-40.4MiB live, 92.4MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
2203(1.2347316233583974e-166 3.241290828799877e-169)0-(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
20-0-(sin.f64 (+.f64 x eps))
00-0-eps
00-0-(+.f64 x eps)
00-0-(sin.f64 x)
00-0-x
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
-.f64(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))cancellation2235
sin.f64(sin.f64 (+.f64 x eps))sensitivity21
Confusion
Predicted +Predicted -
+2230
-231
Precision
0.9911111111111112
Recall
1.0
Confusion?
Predicted +Predicted MaybePredicted -
+22300
-2625
Precision?
0.9653679653679653
Recall?
1.0
Freqs
test
numberfreq
031
1225
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
24.0ms352×0valid
15.0ms158×1valid
0.0ms2valid
Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 24.0ms
ival-add: 9.0ms (37.2% of total)
ival-sin: 9.0ms (37.2% of total)
adjust: 3.0ms (12.4% of total)
ival-sub: 3.0ms (12.4% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

preprocess22.0ms (0.2%)

Memory
17.8MiB live, 17.8MiB allocated
Algorithm
egg-herbie
Rules
102×sub-neg
80×lower-fma.f64
80×lower-fma.f32
68×cancel-sign-sub-inv
64×associate--r+
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01839
13835
28635
316935
431035
536735
644535
748235
849135
067
0107
1137
2187
3247
4327
5477
6807
71077
81517
91667
101747
01747
Stop Event
iter limit
saturated
iter limit
saturated
Calls
Call 1
Inputs
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Outputs
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
Compiler

Compiled 7 to 6 computations (14.3% saved)

eval0.0ms (0%)

Memory
0.2MiB live, 0.2MiB allocated
Compiler

Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory
0.5MiB live, 0.5MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
64.4%
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify6.0ms (0.1%)

Memory
3.4MiB live, 3.4MiB allocated
Algorithm
egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
cost-diff0
(sin.f64 x)
cost-diff0
(+.f64 x eps)
cost-diff0
(sin.f64 (+.f64 x eps))
cost-diff0
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Rules
80×lower-fma.f64
80×lower-fma.f32
48×lower-*.f64
48×lower-*.f32
36×lower-+.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0618
01018
11318
21818
32418
43218
54718
68018
710718
815118
916618
1017418
017418
Stop Event
iter limit
saturated
iter limit
Calls
Call 1
Inputs
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(sin.f64 (+.f64 x eps))
(+.f64 x eps)
x
eps
(sin.f64 x)
Outputs
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(sin.f64 (+.f64 x eps))
(sin.f64 (+.f64 eps x))
(+.f64 x eps)
(+.f64 eps x)
x
eps
(sin.f64 x)

localize29.0ms (0.2%)

Memory
-21.0MiB live, 16.9MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0
(+.f64 x eps)
accuracy0
(sin.f64 x)
accuracy0.09964337851932346
(sin.f64 (+.f64 x eps))
accuracy22.708577793074316
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Samples
15.0ms79×1valid
8.0ms176×0valid
0.0ms2valid
Compiler

Compiled 20 to 8 computations (60% saved)

Precisions
Click to see histograms. Total time spent on operations: 9.0ms
ival-sin: 4.0ms (44.5% of total)
adjust: 2.0ms (22.2% of total)
ival-add: 2.0ms (22.2% of total)
ival-sub: 1.0ms (11.1% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series5.0ms (0%)

Memory
4.1MiB live, 4.1MiB allocated
Counts
4 → 84
Calls
Call 1
Inputs
#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())
#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())
#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())
#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())
Outputs
#s(alt (* eps (cos x)) (taylor 0 eps) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* -1/2 (* eps (sin x))))) (taylor 0 eps) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) (taylor 0 eps) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))) (taylor 0 eps) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor 0 eps) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (+ (sin x) (* eps (cos x))) (taylor 0 eps) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) (taylor 0 eps) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) (taylor 0 eps) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (+ eps x) (taylor 0 eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (+ eps x) (taylor 0 eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (+ eps x) (taylor 0 eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (- (sin (+ eps x)) (sin x)) (taylor inf eps) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (sin (+ eps x)) (sin x)) (taylor inf eps) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (sin (+ eps x)) (sin x)) (taylor inf eps) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (sin (+ eps x)) (sin x)) (taylor inf eps) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (sin (+ eps x)) (taylor inf eps) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (sin (+ eps x)) (taylor inf eps) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (sin (+ eps x)) (taylor inf eps) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (sin (+ eps x)) (taylor inf eps) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt eps (taylor inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (/ x eps))) (taylor inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (/ x eps))) (taylor inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (/ x eps))) (taylor inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (- (sin (- x (* -1 eps))) (sin x)) (taylor -inf eps) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (sin (- x (* -1 eps))) (sin x)) (taylor -inf eps) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (sin (- x (* -1 eps))) (sin x)) (taylor -inf eps) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (sin (- x (* -1 eps))) (sin x)) (taylor -inf eps) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (sin (- x (* -1 eps))) (taylor -inf eps) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (sin (- x (* -1 eps))) (taylor -inf eps) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (sin (- x (* -1 eps))) (taylor -inf eps) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (sin (- x (* -1 eps))) (taylor -inf eps) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt eps (taylor -inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (- (* -1 (/ x eps)) 1))) (taylor -inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (- (* -1 (/ x eps)) 1))) (taylor -inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (- (* -1 (/ x eps)) 1))) (taylor -inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (sin eps) (taylor 0 x) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (sin eps) (* x (- (cos eps) 1))) (taylor 0 x) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) (taylor 0 x) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1))) (taylor 0 x) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (sin eps) (taylor 0 x) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (+ (sin eps) (* x (cos eps))) (taylor 0 x) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps)))))) (taylor 0 x) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps)))))))) (taylor 0 x) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (+ eps x) (taylor 0 x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (+ eps x) (taylor 0 x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (+ eps x) (taylor 0 x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1/6 (pow x 2)))) (taylor 0 x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))) (taylor 0 x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) (taylor 0 x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (- (sin (+ eps x)) (sin x)) (taylor inf x) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (sin (+ eps x)) (sin x)) (taylor inf x) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (sin (+ eps x)) (sin x)) (taylor inf x) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (sin (+ eps x)) (sin x)) (taylor inf x) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (sin (+ eps x)) (taylor inf x) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (sin (+ eps x)) (taylor inf x) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (sin (+ eps x)) (taylor inf x) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (sin (+ eps x)) (taylor inf x) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ eps x))) (taylor inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ eps x))) (taylor inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ eps x))) (taylor inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (- (sin (- eps (* -1 x))) (sin x)) (taylor -inf x) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (sin (- eps (* -1 x))) (sin x)) (taylor -inf x) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (sin (- eps (* -1 x))) (sin x)) (taylor -inf x) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (sin (- eps (* -1 x))) (sin x)) (taylor -inf x) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (sin (- eps (* -1 x))) (taylor -inf x) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (sin (- eps (* -1 x))) (taylor -inf x) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (sin (- eps (* -1 x))) (taylor -inf x) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (sin (- eps (* -1 x))) (taylor -inf x) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ eps x)) 1))) (taylor -inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ eps x)) 1))) (taylor -inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ eps x)) 1))) (taylor -inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor -inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor -inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor -inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor -inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
Calls

6 calls:

TimeVariablePointExpression
1.0ms
eps
@inf
((- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x))
1.0ms
x
@0
((- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x))
1.0ms
eps
@-inf
((- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x))
1.0ms
eps
@0
((- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x))
0.0ms
x
@-inf
((- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x))

simplify144.0ms (1.2%)

Memory
12.4MiB live, 123.0MiB allocated
Algorithm
egg-herbie
Rules
16 678×lower-fma.f64
16 678×lower-fma.f32
4 132×lower-*.f64
4 132×lower-*.f32
2 614×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0107496
1314496
2775489
32829489
46198489
08141458
Stop Event
iter limit
node limit
Counts
84 → 77
Calls
Call 1
Inputs
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(sin x)
(+ (sin x) (* eps (cos x)))
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
x
(+ eps x)
(+ eps x)
(+ eps x)
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
eps
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(sin eps)
(+ (sin eps) (* x (cos eps)))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))
eps
(+ eps x)
(+ eps x)
(+ eps x)
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
x
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
(sin x)
(sin x)
(sin x)
(sin x)
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(sin x)
(sin x)
(sin x)
(sin x)
Outputs
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(*.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(*.f64 (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 (*.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) eps)
(sin x)
(sin.f64 x)
(+ (sin x) (* eps (cos x)))
(fma.f64 (cos.f64 x) eps (sin.f64 x))
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
(fma.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps (sin.f64 x))
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps (sin.f64 x))
x
(+ eps x)
(+.f64 x eps)
(+ eps x)
(+.f64 x eps)
(+ eps x)
(+.f64 x eps)
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(sin (+ eps x))
(sin.f64 (+.f64 x eps))
(sin (+ eps x))
(sin.f64 (+.f64 x eps))
(sin (+ eps x))
(sin.f64 (+.f64 x eps))
(sin (+ eps x))
(sin.f64 (+.f64 x eps))
eps
(* eps (+ 1 (/ x eps)))
(+.f64 x eps)
(* eps (+ 1 (/ x eps)))
(+.f64 x eps)
(* eps (+ 1 (/ x eps)))
(+.f64 x eps)
(- (sin (- x (* -1 eps))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- x (* -1 eps))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- x (* -1 eps))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- x (* -1 eps))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(sin (- x (* -1 eps)))
(sin.f64 (+.f64 x eps))
(sin (- x (* -1 eps)))
(sin.f64 (+.f64 x eps))
(sin (- x (* -1 eps)))
(sin.f64 (+.f64 x eps))
(sin (- x (* -1 eps)))
(sin.f64 (+.f64 x eps))
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(+.f64 x eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(+.f64 x eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(+.f64 x eps)
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(fma.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(fma.f64 (fma.f64 (fma.f64 (fma.f64 (cos.f64 eps) #s(literal -1/6 binary64) #s(literal 1/6 binary64)) x (*.f64 (sin.f64 eps) #s(literal -1/2 binary64))) x (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (cos eps)))
(fma.f64 (cos.f64 eps) x (sin.f64 eps))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (cos.f64 eps)) x (sin.f64 eps))
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))
(fma.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 eps) x) #s(literal -1/6 binary64) (*.f64 (sin.f64 eps) #s(literal -1/2 binary64))) x (cos.f64 eps)) x (sin.f64 eps))
eps
(+ eps x)
(+.f64 x eps)
(+ eps x)
(+.f64 x eps)
(+ eps x)
(+.f64 x eps)
x
(* x (+ 1 (* -1/6 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/6 binary64) x)
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x) #s(literal -1/6 binary64)) x)
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(sin (+ eps x))
(sin.f64 (+.f64 x eps))
(sin (+ eps x))
(sin.f64 (+.f64 x eps))
(sin (+ eps x))
(sin.f64 (+.f64 x eps))
(sin (+ eps x))
(sin.f64 (+.f64 x eps))
x
(* x (+ 1 (/ eps x)))
(+.f64 x eps)
(* x (+ 1 (/ eps x)))
(+.f64 x eps)
(* x (+ 1 (/ eps x)))
(+.f64 x eps)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(sin (- eps (* -1 x)))
(sin.f64 (+.f64 x eps))
(sin (- eps (* -1 x)))
(sin.f64 (+.f64 x eps))
(sin (- eps (* -1 x)))
(sin.f64 (+.f64 x eps))
(sin (- eps (* -1 x)))
(sin.f64 (+.f64 x eps))
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(+.f64 x eps)
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(+.f64 x eps)
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(+.f64 x eps)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)

rewrite172.0ms (1.4%)

Memory
17.0MiB live, 136.3MiB allocated
Rules
4 986×lower-fma.f64
4 986×lower-fma.f32
4 676×lower-*.f64
4 676×lower-*.f32
2 176×lower-/.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0616
01016
15316
238016
3476616
0821016
Stop Event
iter limit
node limit
iter limit
Counts
4 → 214
Calls
Call 1
Inputs
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(sin.f64 (+.f64 x eps))
(+.f64 x eps)
(sin.f64 x)
Outputs
(*.f64 (pow.f64 (/.f64 (fma.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (sin.f64 x) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64))) (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 6 binary64)) (pow.f64 (sin.f64 x) #s(literal 6 binary64)))) #s(literal -1 binary64)) (pow.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (fma.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (sin.f64 x) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64))) (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 9 binary64)) (pow.f64 (sin.f64 x) #s(literal 9 binary64)))) #s(literal -1 binary64)) (pow.f64 (+.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 6 binary64)) (+.f64 (pow.f64 (*.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 6 binary64)))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)))) #s(literal -1 binary64)) (pow.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 6 binary64)) (pow.f64 (sin.f64 x) #s(literal 6 binary64)))) #s(literal -1 binary64)) (pow.f64 (+.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64))) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 4 binary64))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) #s(literal -1 binary64)) (pow.f64 (/.f64 (*.f64 (cos.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal -2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))) (-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))) #s(literal -1 binary64)))
(*.f64 (/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 4 binary64)) (pow.f64 (*.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (sin.f64 x)) #s(literal 2 binary64)))) (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (*.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (sin.f64 x))))
(*.f64 (/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (sin.f64 x)) #s(literal 3 binary64)) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 6 binary64)))) (fma.f64 (*.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (sin.f64 x)) (-.f64 (*.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (sin.f64 x)) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64))) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 4 binary64))))
(*.f64 (/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) (-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)))
(*.f64 (/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64)))) (fma.f64 (sin.f64 x) (-.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64))))
(*.f64 (*.f64 #s(literal 2 binary64) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))))
(*.f64 (/.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) #s(literal 2 binary64)) (/.f64 (-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) (*.f64 (cos.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal -2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))))))
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(*.f64 (pow.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) #s(literal -1 binary64)) (pow.f64 (pow.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) #s(literal -1 binary64)) (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))))
(*.f64 (pow.f64 (fma.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (sin.f64 x) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (pow.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) #s(literal -1 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (fma.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (sin.f64 x) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64))) #s(literal -1 binary64)) (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))))
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(exp.f64 (*.f64 (log.f64 (sin.f64 (+.f64 eps x))) #s(literal 1 binary64)))
(*.f64 (pow.f64 (/.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64)))) #s(literal -1 binary64)) (pow.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)) (+.f64 (pow.f64 eps #s(literal 9 binary64)) (pow.f64 x #s(literal 9 binary64)))) #s(literal -1 binary64)) (pow.f64 (-.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (*.f64 eps x) #s(literal 3 binary64))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (-.f64 x eps) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 eps #s(literal 4 binary64)))) #s(literal -1 binary64)) (pow.f64 (fma.f64 eps eps (*.f64 x x)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (-.f64 x eps) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64)))) #s(literal -1 binary64)) (pow.f64 (fma.f64 (*.f64 eps eps) (fma.f64 eps eps (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)))
(*.f64 (/.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (fma.f64 eps (+.f64 eps x) (*.f64 x x)))
(*.f64 (/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 (-.f64 eps x) eps) #s(literal 2 binary64)))) (-.f64 (*.f64 x x) (*.f64 (-.f64 eps x) eps)))
(*.f64 (/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (-.f64 eps x) eps) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (*.f64 (-.f64 eps x) eps) (-.f64 (*.f64 (-.f64 eps x) eps) (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))))
(*.f64 (/.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)) (*.f64 (-.f64 x eps) (+.f64 eps x))) (+.f64 eps x))
(*.f64 (*.f64 (+.f64 eps x) (-.f64 eps x)) (pow.f64 (-.f64 eps x) #s(literal -1 binary64)))
(*.f64 (pow.f64 (-.f64 x eps) #s(literal -1 binary64)) (pow.f64 (pow.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)) #s(literal -1 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (-.f64 x eps) #s(literal -1 binary64)) (*.f64 (-.f64 x eps) (+.f64 eps x)))
(*.f64 (pow.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal -1 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)) #s(literal -1 binary64)) (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))
(*.f64 #s(literal 1 binary64) (+.f64 eps x))
(*.f64 (neg.f64 (*.f64 (-.f64 x eps) (+.f64 eps x))) (pow.f64 (neg.f64 (-.f64 x eps)) #s(literal -1 binary64)))
(*.f64 (neg.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (pow.f64 (neg.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x))) #s(literal -1 binary64)))
(*.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)) (pow.f64 (-.f64 x eps) #s(literal -1 binary64)))
(*.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)) (/.f64 (+.f64 eps x) (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(*.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)) (*.f64 (+.f64 eps x) (pow.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)) #s(literal -1 binary64))))
(*.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)) #s(literal -1 binary64)))
(*.f64 (+.f64 eps x) (/.f64 (-.f64 x eps) (-.f64 x eps)))
(*.f64 (+.f64 eps x) (*.f64 (-.f64 x eps) (pow.f64 (-.f64 x eps) #s(literal -1 binary64))))
(pow.f64 (/.f64 (-.f64 eps x) (*.f64 (+.f64 eps x) (-.f64 eps x))) #s(literal -1 binary64))
(pow.f64 (/.f64 (pow.f64 (+.f64 eps x) #s(literal -1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (pow.f64 (+.f64 eps x) #s(literal -1 binary64)) #s(literal -1 binary64))
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 eps #s(literal 4 binary64))) (pow.f64 (-.f64 x eps) #s(literal -1 binary64))) (fma.f64 eps eps (*.f64 x x)))
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (-.f64 x eps) #s(literal -1 binary64))) (fma.f64 (*.f64 eps eps) (fma.f64 eps eps (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))))
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)) #s(literal -1 binary64))) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))))
(/.f64 (*.f64 (+.f64 (pow.f64 eps #s(literal 9 binary64)) (pow.f64 x #s(literal 9 binary64))) (pow.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)) #s(literal -1 binary64))) (-.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (*.f64 eps x) #s(literal 3 binary64))))
(/.f64 (-.f64 (pow.f64 (*.f64 x (/.f64 x (-.f64 x eps))) #s(literal 2 binary64)) (pow.f64 (*.f64 eps (/.f64 eps (-.f64 x eps))) #s(literal 2 binary64))) (fma.f64 x (/.f64 x (-.f64 x eps)) (*.f64 eps (/.f64 eps (-.f64 x eps)))))
(/.f64 (-.f64 (*.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (-.f64 x eps) #s(literal -3 binary64))) (*.f64 (pow.f64 eps #s(literal 6 binary64)) (pow.f64 (-.f64 x eps) #s(literal -3 binary64)))) (+.f64 (pow.f64 (*.f64 x (/.f64 x (-.f64 x eps))) #s(literal 2 binary64)) (+.f64 (pow.f64 (*.f64 eps (/.f64 eps (-.f64 x eps))) #s(literal 2 binary64)) (*.f64 (*.f64 x (/.f64 x (-.f64 x eps))) (*.f64 eps (/.f64 eps (-.f64 x eps)))))))
(/.f64 (neg.f64 (*.f64 (+.f64 eps x) (-.f64 eps x))) (neg.f64 (-.f64 eps x)))
(/.f64 (neg.f64 (neg.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)))) (neg.f64 (neg.f64 (-.f64 x eps))))
(/.f64 (neg.f64 (neg.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (neg.f64 (neg.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)))))
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 eps #s(literal 4 binary64))) #s(literal 1 binary64)) (*.f64 (fma.f64 eps eps (*.f64 x x)) (-.f64 x eps)))
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) #s(literal 1 binary64)) (*.f64 (fma.f64 (*.f64 eps eps) (fma.f64 eps eps (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))) (-.f64 x eps)))
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) #s(literal 1 binary64)) (*.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(/.f64 (*.f64 (+.f64 (pow.f64 eps #s(literal 9 binary64)) (pow.f64 x #s(literal 9 binary64))) #s(literal 1 binary64)) (*.f64 (-.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (*.f64 eps x) #s(literal 3 binary64))) (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(/.f64 (*.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x)))
(/.f64 (-.f64 (*.f64 (*.f64 x x) (-.f64 x eps)) (*.f64 (-.f64 x eps) (*.f64 eps eps))) (pow.f64 (-.f64 x eps) #s(literal 2 binary64)))
(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 eps #s(literal 4 binary64))) (*.f64 (-.f64 x eps) (fma.f64 eps eps (*.f64 x x))))
(/.f64 (*.f64 (+.f64 eps x) (-.f64 eps x)) (-.f64 eps x))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (*.f64 (-.f64 x eps) (fma.f64 (*.f64 eps eps) (fma.f64 eps eps (*.f64 x x)) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (*.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (+.f64 eps x) #s(literal -1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 eps x) (*.f64 (+.f64 eps x) (-.f64 eps x))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (+.f64 eps x) #s(literal -1 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 eps x) #s(literal -1 binary64)))
(/.f64 (+.f64 (pow.f64 eps #s(literal 9 binary64)) (pow.f64 x #s(literal 9 binary64))) (*.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)) (-.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (*.f64 eps x) #s(literal 3 binary64)))))
(/.f64 (neg.f64 (*.f64 (-.f64 x eps) (+.f64 eps x))) (neg.f64 (-.f64 x eps)))
(/.f64 (neg.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(/.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)) (-.f64 x eps))
(/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (-.f64 eps x) eps (*.f64 x x)))
(neg.f64 (/.f64 (neg.f64 (*.f64 (-.f64 x eps) (+.f64 eps x))) (-.f64 x eps)))
(neg.f64 (/.f64 (neg.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(neg.f64 (/.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)) (neg.f64 (-.f64 x eps))))
(neg.f64 (/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (neg.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)))))
(fma.f64 (/.f64 (*.f64 x x) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (fma.f64 eps (+.f64 eps x) (*.f64 x x)) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))))
(fma.f64 (/.f64 (*.f64 x x) (*.f64 (-.f64 x eps) (+.f64 eps x))) (+.f64 eps x) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))))
(fma.f64 (*.f64 x x) (pow.f64 (-.f64 x eps) #s(literal -1 binary64)) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))))
(fma.f64 x (/.f64 x (-.f64 x eps)) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))))
(-.f64 (/.f64 (*.f64 eps eps) (-.f64 eps x)) (/.f64 (*.f64 x x) (-.f64 eps x)))
(-.f64 (*.f64 x (/.f64 x (-.f64 x eps))) (*.f64 eps (/.f64 eps (-.f64 x eps))))
(+.f64 (*.f64 x (/.f64 x (-.f64 x eps))) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))))
(+.f64 eps x)
(+.f64 x eps)
(exp.f64 (*.f64 (log.f64 (pow.f64 (+.f64 eps x) #s(literal -1 binary64))) #s(literal -1 binary64)))
(pow.f64 (sin.f64 x) #s(literal 1 binary64))
(sin.f64 x)
(exp.f64 (*.f64 (log.f64 (sin.f64 x)) #s(literal 1 binary64)))

eval37.0ms (0.3%)

Memory
-8.1MiB live, 64.7MiB allocated
Compiler

Compiled 6 625 to 852 computations (87.1% saved)

prune9.0ms (0.1%)

Memory
-13.4MiB live, 25.4MiB allocated
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New2856291
Fresh000
Picked011
Done000
Total2857292
Accuracy
100.0%
Counts
292 → 7
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.8%
(fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (cos.f64 eps) (sin.f64 x) (neg.f64 (sin.f64 x))))
64.4%
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
100.0%
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
98.9%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps))
98.8%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps))
98.5%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
98.2%
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
Compiler

Compiled 137 to 112 computations (18.2% saved)

simplify243.0ms (2%)

Memory
-1.5MiB live, 118.7MiB allocated
Algorithm
egg-herbie
Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
cost-diff0
(fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64)))
cost-diff0
(fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x))
cost-diff0
(*.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
cost-diff0
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps))
cost-diff0
(*.f64 (sin.f64 x) #s(literal -1/2 binary64))
cost-diff0
(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x))
cost-diff0
(*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
cost-diff0
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps))
cost-diff0
(cos.f64 x)
cost-diff0
(*.f64 (cos.f64 x) eps)
cost-diff0
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
cost-diff0
(sin.f64 eps)
cost-diff0
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
cost-diff0
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
cost-diff128
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
cost-diff192
(+.f64 #s(literal 0 binary64) eps)
cost-diff576
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))
Rules
4 688×lower-fma.f32
4 680×lower-fma.f64
2 656×lower-*.f32
2 642×lower-*.f64
1 462×associate-*l/
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
034221
056211
189211
2190211
3451211
4625211
5738211
6817211
7851211
8987211
91022211
101249211
111600211
121943211
132677211
143219211
153371208
163489208
173610208
183946208
194893208
205975208
216213208
226429208
236507208
246531208
256585208
267602208
277982208
08044206
Stop Event
iter limit
node limit
iter limit
Calls
Call 1
Inputs
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64))
(sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))
#s(literal 1/2 binary64)
(+.f64 #s(literal 0 binary64) eps)
#s(literal 0 binary64)
eps
#s(literal 2 binary64)
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))
(fma.f64 #s(literal 2 binary64) x eps)
x
#s(literal -2 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
(sin.f64 eps)
eps
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
(*.f64 (cos.f64 x) eps)
(cos.f64 x)
x
eps
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps))
(*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x))
(*.f64 (sin.f64 x) #s(literal -1/2 binary64))
(sin.f64 x)
x
#s(literal -1/2 binary64)
eps
(cos.f64 x)
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps))
(*.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x))
(fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64)))
#s(literal -1/6 binary64)
(*.f64 (cos.f64 x) eps)
(cos.f64 x)
x
eps
(*.f64 (sin.f64 x) #s(literal -1/2 binary64))
(sin.f64 x)
#s(literal -1/2 binary64)
Outputs
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) #s(literal -2 binary64)))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64))
(*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) #s(literal -2 binary64))
(sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))
(*.f64 eps #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(+.f64 #s(literal 0 binary64) eps)
eps
#s(literal 0 binary64)
eps
#s(literal 2 binary64)
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))
(neg.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(fma.f64 #s(literal 2 binary64) x eps)
(fma.f64 x #s(literal 2 binary64) eps)
x
#s(literal -2 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
(sin.f64 eps)
eps
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
(*.f64 (cos.f64 x) eps)
(cos.f64 x)
x
eps
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x)) eps))
(*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x)) eps)
(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x))
(*.f64 (sin.f64 x) #s(literal -1/2 binary64))
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
(sin.f64 x)
x
#s(literal -1/2 binary64)
eps
(cos.f64 x)
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
(*.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(*.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)
(fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x))
(fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x))
(fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64)))
(fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))
#s(literal -1/6 binary64)
(*.f64 (cos.f64 x) eps)
(cos.f64 x)
x
eps
(*.f64 (sin.f64 x) #s(literal -1/2 binary64))
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
(sin.f64 x)
#s(literal -1/2 binary64)

localize151.0ms (1.3%)

Memory
23.0MiB live, 225.2MiB allocated
Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
accuracy0.0078125
(fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x))
accuracy0.0078125
(fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64)))
accuracy0.01171875
(*.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
accuracy0.6894019019108873
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps))
accuracy0
(sin.f64 x)
accuracy0
(cos.f64 x)
accuracy0.022684980164287515
(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x))
accuracy0.7730052602805118
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps))
accuracy0
(cos.f64 x)
accuracy0.00390625
(*.f64 (cos.f64 x) eps)
accuracy0.9517168949891799
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
accuracy0
(sin.f64 eps)
accuracy1.123839090955632
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
accuracy0
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))
accuracy0
(sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))
accuracy0.00390625
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
accuracy0.03142341452874396
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
Samples
86.0ms78×1valid
39.0ms177×0valid
2.0ms3valid
Compiler

Compiled 198 to 35 computations (82.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 101.0ms
ival-mult: 53.0ms (52.2% of total)
ival-cos: 15.0ms (14.8% of total)
adjust: 9.0ms (8.9% of total)
ival-add: 8.0ms (7.9% of total)
ival-sin: 8.0ms (7.9% of total)
const: 4.0ms (3.9% of total)
ival-div: 2.0ms (2% of total)
ival-sub: 2.0ms (2% of total)
exact: 1.0ms (1% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series56.0ms (0.5%)

Memory
-27.5MiB live, 59.4MiB allocated
Counts
20 → 396
Calls
Call 1
Inputs
#s(alt (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) (patch (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) #<representation binary64>) () ())
#s(alt (+.f64 #s(literal 0 binary64) eps) (patch (+.f64 #s(literal 0 binary64) eps) #<representation binary64>) () ())
#s(alt (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (patch (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) #<representation binary64>) () ())
#s(alt (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) (patch (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) #<representation binary64>) () ())
#s(alt (sin.f64 eps) (patch (sin.f64 eps) #<representation binary64>) () ())
#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) #<representation binary64>) () ())
#s(alt (*.f64 (cos.f64 x) eps) (patch (*.f64 (cos.f64 x) eps) #<representation binary64>) () ())
#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())
#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)) #<representation binary64>) () ())
#s(alt (*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps) (patch (*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps) #<representation binary64>) () ())
#s(alt (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) (patch (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) #<representation binary64>) () ())
#s(alt (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) (patch (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)) #<representation binary64>) () ())
#s(alt (*.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps) (patch (*.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps) #<representation binary64>) () ())
#s(alt (fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) (patch (fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) (patch (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) #<representation binary64>) () ())
#s(alt (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) (patch (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #<representation binary64>) () ())
#s(alt (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)) (patch (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)) #<representation binary64>) () ())
#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())
Outputs
#s(alt (* -1 x) (taylor 0 eps) (#s(alt (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) (patch (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 x) (* -1/2 eps)) (taylor 0 eps) (#s(alt (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) (patch (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 x) (* -1/2 eps)) (taylor 0 eps) (#s(alt (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) (patch (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 x) (* -1/2 eps)) (taylor 0 eps) (#s(alt (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) (patch (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 eps) (#s(alt (+.f64 #s(literal 0 binary64) eps) (patch (+.f64 #s(literal 0 binary64) eps) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 eps) (#s(alt (+.f64 #s(literal 0 binary64) eps) (patch (+.f64 #s(literal 0 binary64) eps) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 eps) (#s(alt (+.f64 #s(literal 0 binary64) eps) (patch (+.f64 #s(literal 0 binary64) eps) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 eps) (#s(alt (+.f64 #s(literal 0 binary64) eps) (patch (+.f64 #s(literal 0 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (cos (* -1 x)) (taylor 0 eps) (#s(alt (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (patch (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))) (taylor 0 eps) (#s(alt (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (patch (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x)))))) (taylor 0 eps) (#s(alt (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (patch (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x)))))) (taylor 0 eps) (#s(alt (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (patch (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* eps (cos (* -1 x))) (taylor 0 eps) (#s(alt (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) (patch (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))) (taylor 0 eps) (#s(alt (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) (patch (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))) (taylor 0 eps) (#s(alt (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) (patch (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))) (taylor 0 eps) (#s(alt (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) (patch (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* eps (cos x)) (taylor 0 eps) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* -1/2 (* eps (sin x))))) (taylor 0 eps) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) (taylor 0 eps) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))) (taylor 0 eps) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 eps) (#s(alt (sin.f64 eps) (patch (sin.f64 eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (* -1/6 (pow eps 2)))) (taylor 0 eps) (#s(alt (sin.f64 eps) (patch (sin.f64 eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6)))) (taylor 0 eps) (#s(alt (sin.f64 eps) (patch (sin.f64 eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6)))) (taylor 0 eps) (#s(alt (sin.f64 eps) (patch (sin.f64 eps) #<representation binary64>) () ())) ())
#s(alt (* eps (cos x)) (taylor 0 eps) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* -1/2 (* eps (sin x))))) (taylor 0 eps) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) (taylor 0 eps) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))) (taylor 0 eps) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) #<representation binary64>) () ())) ())
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#s(alt (- (sin (- eps (* -1 x))) (sin x)) (taylor -inf x) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) (taylor -inf x) (#s(alt (*.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps) (patch (*.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) (taylor -inf x) (#s(alt (*.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps) (patch (*.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) (taylor -inf x) (#s(alt (*.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps) (patch (*.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) (taylor -inf x) (#s(alt (*.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps) (patch (*.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) (patch (fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) (patch (fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) (patch (fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) (patch (fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))) (taylor -inf x) (#s(alt (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) (patch (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))) (taylor -inf x) (#s(alt (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) (patch (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))) (taylor -inf x) (#s(alt (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) (patch (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))) (taylor -inf x) (#s(alt (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) (patch (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor -inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor -inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor -inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor -inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
Calls

6 calls:

TimeVariablePointExpression
6.0ms
eps
@0
((/ (+ (* 2 x) eps) -2) (+ 0 eps) (cos (/ (+ (* 2 x) eps) -2)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (sin x) -1/2) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (sin (* 1/2 (+ 0 eps))) (* 1/2 (+ 0 eps)) (sin x))
4.0ms
x
@0
((/ (+ (* 2 x) eps) -2) (+ 0 eps) (cos (/ (+ (* 2 x) eps) -2)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (sin x) -1/2) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (sin (* 1/2 (+ 0 eps))) (* 1/2 (+ 0 eps)) (sin x))
4.0ms
eps
@inf
((/ (+ (* 2 x) eps) -2) (+ 0 eps) (cos (/ (+ (* 2 x) eps) -2)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (sin x) -1/2) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (sin (* 1/2 (+ 0 eps))) (* 1/2 (+ 0 eps)) (sin x))
4.0ms
x
@inf
((/ (+ (* 2 x) eps) -2) (+ 0 eps) (cos (/ (+ (* 2 x) eps) -2)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (sin x) -1/2) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (sin (* 1/2 (+ 0 eps))) (* 1/2 (+ 0 eps)) (sin x))
4.0ms
eps
@-inf
((/ (+ (* 2 x) eps) -2) (+ 0 eps) (cos (/ (+ (* 2 x) eps) -2)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (sin x) -1/2) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (sin (* 1/2 (+ 0 eps))) (* 1/2 (+ 0 eps)) (sin x))

simplify222.0ms (1.9%)

Memory
36.7MiB live, 149.5MiB allocated
Algorithm
egg-herbie
Rules
14 482×lower-fma.f64
14 482×lower-fma.f32
5 858×lower-*.f64
5 858×lower-*.f32
3 914×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03833943
111723693
232753605
379463605
082053345
Stop Event
iter limit
node limit
Counts
396 → 380
Calls
Call 1
Inputs
(* -1 x)
(+ (* -1 x) (* -1/2 eps))
(+ (* -1 x) (* -1/2 eps))
(+ (* -1 x) (* -1/2 eps))
eps
eps
eps
eps
(cos (* -1 x))
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))
(+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x))))))
(+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x))))))
(* eps (cos (* -1 x)))
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))))
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(* -1/2 (sin x))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* -1/2 eps)
(* eps (- (* -1 (/ x eps)) 1/2))
(* eps (- (* -1 (/ x eps)) 1/2))
(* eps (- (* -1 (/ x eps)) 1/2))
eps
eps
eps
eps
(cos (* -1/2 (+ eps (* 2 x))))
(cos (* -1/2 (+ eps (* 2 x))))
(cos (* -1/2 (+ eps (* 2 x))))
(cos (* -1/2 (+ eps (* 2 x))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps (sin x)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* -1/6 (* (pow eps 3) (cos x)))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* -1/6 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* -1/6 (* eps (cos x)))
(* eps (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* eps (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* eps (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* -1/2 eps)
(* -1 (* eps (+ 1/2 (/ x eps))))
(* -1 (* eps (+ 1/2 (/ x eps))))
(* -1 (* eps (+ 1/2 (/ x eps))))
eps
eps
eps
eps
(cos (* -1/2 (- (* 2 x) (* -1 eps))))
(cos (* -1/2 (- (* 2 x) (* -1 eps))))
(cos (* -1/2 (- (* 2 x) (* -1 eps))))
(cos (* -1/2 (- (* 2 x) (* -1 eps))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps (sin x)))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(* -1/6 (* (pow eps 3) (cos x)))
(* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))
(* -1/6 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))
(* -1/6 (* eps (cos x)))
(* -1 (* eps (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))
(* -1 (* eps (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))
(* -1 (* eps (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* -1/2 eps)
(+ (* -1 x) (* -1/2 eps))
(+ (* -1 x) (* -1/2 eps))
(+ (* -1 x) (* -1/2 eps))
(cos (* -1/2 eps))
(+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps))))
(+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (* -1 (sin (* -1/2 eps))))))
(+ (cos (* -1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* -1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps)))))) (* -1 (sin (* -1/2 eps))))))
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* x (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* -1/3 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))))))))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
1
(+ 1 (* -1/2 (* eps x)))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(* -1/2 x)
(* x (- (* 1/12 (pow x 2)) 1/2))
(* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))
(* x (- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/10080 (pow x 2)) 1/240)))) 1/2))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* 1/12 (* (pow eps 2) x)) (* eps (- (* 1/12 (pow eps 2)) 1/2)))))))
(+ 1 (* -1/6 (pow eps 2)))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2))))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2))))))
(* -1/6 eps)
(+ (* -1/2 x) (* -1/6 eps))
(+ (* -1/6 eps) (* x (- (* 1/12 (* eps x)) 1/2)))
(+ (* -1/6 eps) (* x (- (* x (+ (* 1/12 eps) (* 1/12 x))) 1/2)))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(* -1 x)
(* x (- (* -1/2 (/ eps x)) 1))
(* x (- (* -1/2 (/ eps x)) 1))
(* x (- (* -1/2 (/ eps x)) 1))
(cos (* -1/2 (+ eps (* 2 x))))
(cos (* -1/2 (+ eps (* 2 x))))
(cos (* -1/2 (+ eps (* 2 x))))
(cos (* -1/2 (+ eps (* 2 x))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(cos x)
(cos x)
(cos x)
(cos x)
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(sin x)
(sin x)
(sin x)
(sin x)
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ eps x)))))
(* -1 (* x (+ 1 (* 1/2 (/ eps x)))))
(* -1 (* x (+ 1 (* 1/2 (/ eps x)))))
(cos (* -1/2 (- eps (* -2 x))))
(cos (* -1/2 (- eps (* -2 x))))
(cos (* -1/2 (- eps (* -2 x))))
(cos (* -1/2 (- eps (* -2 x))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(cos x)
(cos x)
(cos x)
(cos x)
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(sin x)
(sin x)
(sin x)
(sin x)
Outputs
(* -1 x)
(neg.f64 x)
(+ (* -1 x) (* -1/2 eps))
(fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))
(+ (* -1 x) (* -1/2 eps))
(fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))
(+ (* -1 x) (* -1/2 eps))
(fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))
eps
eps
eps
eps
(cos (* -1 x))
(cos.f64 x)
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x))
(+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x))))))
(fma.f64 (fma.f64 (sin.f64 x) #s(literal -1/2 binary64) (*.f64 (*.f64 (cos.f64 x) #s(literal -1/8 binary64)) eps)) eps (cos.f64 x))
(+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x))))))
(fma.f64 (fma.f64 (neg.f64 (sin.f64 x)) (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) (*.f64 (*.f64 (cos.f64 x) #s(literal -1/8 binary64)) eps)) eps (cos.f64 x))
(* eps (cos (* -1 x)))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))))
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))
(*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))))
(*.f64 (fma.f64 (fma.f64 (neg.f64 (sin.f64 x)) (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 #s(literal -1/24 binary64) eps))) (*.f64 (*.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(*.f64 (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 eps (*.f64 #s(literal 1/24 binary64) eps) #s(literal -1/2 binary64)) (*.f64 (*.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) eps)
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64) eps)
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 eps eps) #s(literal -1/6 binary64)) eps)
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 eps eps) #s(literal 1/120 binary64)) (*.f64 eps eps) #s(literal -1/6 binary64)) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(*.f64 (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 eps (*.f64 #s(literal 1/24 binary64) eps) #s(literal -1/2 binary64)) (*.f64 (*.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(*.f64 (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 eps (*.f64 #s(literal 1/24 binary64) eps) #s(literal -1/2 binary64)) (*.f64 (*.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(cos x)
(cos.f64 x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x))
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(*.f64 (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 eps (*.f64 #s(literal 1/24 binary64) eps) #s(literal -1/2 binary64)) (*.f64 (*.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
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(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(fma.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(fma.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(fma.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(fma.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(fma.f64 (*.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 (sin.f64 x) #s(literal -1/2 binary64)))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(fma.f64 (*.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 (sin.f64 x) #s(literal -1/2 binary64)))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(fma.f64 (*.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 (sin.f64 x) #s(literal -1/2 binary64)))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(fma.f64 (*.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 (sin.f64 x) #s(literal -1/2 binary64)))
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* 1/2 (/ eps x)))))
(*.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)) (neg.f64 x))
(* -1 (* x (+ 1 (* 1/2 (/ eps x)))))
(*.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)) (neg.f64 x))
(* -1 (* x (+ 1 (* 1/2 (/ eps x)))))
(*.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)) (neg.f64 x))
(cos (* -1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))
(cos (* -1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))
(cos (* -1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))
(cos (* -1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x))
(* -1/2 (sin x))
(*.f64 (sin.f64 x) #s(literal -1/2 binary64))
(* -1/2 (sin x))
(*.f64 (sin.f64 x) #s(literal -1/2 binary64))
(* -1/2 (sin x))
(*.f64 (sin.f64 x) #s(literal -1/2 binary64))
(* -1/2 (sin x))
(*.f64 (sin.f64 x) #s(literal -1/2 binary64))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(fma.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(fma.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(fma.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(fma.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(fma.f64 (*.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 (sin.f64 x) #s(literal -1/2 binary64)))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(fma.f64 (*.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 (sin.f64 x) #s(literal -1/2 binary64)))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(fma.f64 (*.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 (sin.f64 x) #s(literal -1/2 binary64)))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(fma.f64 (*.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 (sin.f64 x) #s(literal -1/2 binary64)))
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)

rewrite209.0ms (1.7%)

Memory
-20.8MiB live, 208.2MiB allocated
Rules
6 402×lower-fma.f32
6 394×lower-fma.f64
4 248×lower-/.f32
4 246×lower-/.f64
3 946×lower-*.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
034179
056171
1188171
21555171
08255171
Stop Event
iter limit
node limit
iter limit
Counts
20 → 631
Calls
Call 1
Inputs
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))
(+.f64 #s(literal 0 binary64) eps)
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
(sin.f64 eps)
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
(*.f64 (cos.f64 x) eps)
(cos.f64 x)
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps))
(*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x))
(*.f64 (sin.f64 x) #s(literal -1/2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps))
(*.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x))
(fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64)))
(sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))
(sin.f64 x)
Outputs
(*.f64 (/.f64 (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))))) #s(literal -2 binary64)) (/.f64 (fma.f64 x #s(literal 2 binary64) eps) (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64)))))))
(*.f64 (pow.f64 (/.f64 #s(literal -2 binary64) (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 (neg.f64 eps) eps))) #s(literal -1 binary64)) (pow.f64 (-.f64 (*.f64 x #s(literal 2 binary64)) eps) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal -2 binary64) (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) #s(literal -1 binary64)) (pow.f64 (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))))) #s(literal -1 binary64)))
(*.f64 (*.f64 (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 (neg.f64 eps) eps)) #s(literal -1/2 binary64)) (pow.f64 (-.f64 (*.f64 x #s(literal 2 binary64)) eps) #s(literal -1 binary64)))
(*.f64 (*.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) #s(literal -1/2 binary64)) (pow.f64 (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))))) #s(literal -1 binary64)))
(*.f64 (neg.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps))) #s(literal -1/2 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (/.f64 #s(literal -2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))))
(*.f64 #s(literal -1 binary64) (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))
(*.f64 (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 (neg.f64 eps) eps)) (/.f64 #s(literal 1 binary64) (*.f64 #s(literal -2 binary64) (-.f64 (*.f64 x #s(literal 2 binary64)) eps))))
(*.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))
(*.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 #s(literal -2 binary64) (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))))))))
(*.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) #s(literal 1/2 binary64))
(*.f64 #s(literal -1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))
(*.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)) (/.f64 (-.f64 (*.f64 x #s(literal 2 binary64)) eps) (-.f64 (*.f64 x #s(literal 2 binary64)) eps)))
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal -1/2 binary64))
(pow.f64 (/.f64 #s(literal -2 binary64) (fma.f64 x #s(literal 2 binary64) eps)) #s(literal -1 binary64))
(/.f64 (neg.f64 (*.f64 (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 (neg.f64 eps) eps)) #s(literal -1/2 binary64))) (neg.f64 (-.f64 (*.f64 x #s(literal 2 binary64)) eps)))
(/.f64 (neg.f64 (*.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) #s(literal -1/2 binary64))) (neg.f64 (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64)))))))
(/.f64 (neg.f64 (neg.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)))) #s(literal 2 binary64))
(/.f64 (*.f64 (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 (neg.f64 eps) eps)) #s(literal -1/2 binary64)) (-.f64 (*.f64 x #s(literal 2 binary64)) eps))
(/.f64 (*.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) #s(literal -1/2 binary64)) (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))))))
(/.f64 (neg.f64 (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 (neg.f64 eps) eps))) (neg.f64 (*.f64 #s(literal -2 binary64) (-.f64 (*.f64 x #s(literal 2 binary64)) eps))))
(/.f64 (neg.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (neg.f64 (*.f64 #s(literal -2 binary64) (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))))))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps))) #s(literal -2 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal -2 binary64) (fma.f64 x #s(literal 2 binary64) eps))))
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(+.f64 (/.f64 (pow.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps)) #s(literal 2 binary64)) (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 #s(literal 1/2 binary64) (sin.f64 x)))) (neg.f64 (/.f64 (pow.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) #s(literal 2 binary64)) (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 #s(literal 1/2 binary64) (sin.f64 x))))))
(+.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps)) (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))
(+.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps)))
(/.f64 (+.f64 (pow.f64 (*.f64 #s(literal 0 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 3 binary64)) (pow.f64 (*.f64 #s(literal 1 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 3 binary64))) (fma.f64 (*.f64 #s(literal 0 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 #s(literal 0 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (-.f64 (*.f64 (*.f64 #s(literal 1 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 #s(literal 1 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) (*.f64 (*.f64 #s(literal 0 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 #s(literal 1 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))))))
(fma.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 1 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 0 binary64)))
(fma.f64 #s(literal 0 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 1 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(+.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 1 binary64)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 0 binary64)))
(+.f64 (*.f64 #s(literal 0 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 #s(literal 1 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(*.f64 (/.f64 #s(literal 1/2 binary64) eps) (/.f64 (pow.f64 eps #s(literal 3 binary64)) eps))
(*.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) eps) (/.f64 #s(literal 1/2 binary64) eps))
(*.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(literal 1/2 binary64)) (pow.f64 (neg.f64 eps) #s(literal -1 binary64)))
(*.f64 (*.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/2 binary64)) (pow.f64 eps #s(literal -2 binary64)))
(*.f64 (*.f64 #s(literal 1/2 binary64) (neg.f64 (*.f64 eps eps))) (pow.f64 (neg.f64 eps) #s(literal -1 binary64)))
(*.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 eps #s(literal 3 binary64))) (pow.f64 eps #s(literal -2 binary64)))
(*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 #s(literal 1/2 binary64) eps) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/2 binary64) eps))))
(*.f64 (+.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/8 binary64) (pow.f64 eps #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 0 binary64) (-.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) eps) #s(literal 2 binary64)) (*.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/2 binary64) eps))))))
(*.f64 #s(literal 1/2 binary64) eps)
(*.f64 eps #s(literal 1/2 binary64))
(/.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 eps #s(literal 3 binary64)) #s(literal 0 binary64)) (+.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) eps) #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 #s(literal 1/2 binary64) eps) #s(literal 0 binary64)))))
(/.f64 (neg.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(literal 1/2 binary64))) (neg.f64 (neg.f64 eps)))
(/.f64 (neg.f64 (*.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/2 binary64))) (neg.f64 (*.f64 eps eps)))
(/.f64 (neg.f64 (*.f64 #s(literal 1/2 binary64) (neg.f64 (*.f64 eps eps)))) (neg.f64 (neg.f64 eps)))
(/.f64 (neg.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 eps #s(literal 3 binary64)))) (neg.f64 (*.f64 eps eps)))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 #s(literal 1/2 binary64) eps) #s(literal 2 binary64)))) (neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/2 binary64) eps))))
(/.f64 (neg.f64 (+.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/8 binary64) (pow.f64 eps #s(literal 3 binary64))))) (neg.f64 (+.f64 #s(literal 0 binary64) (-.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) eps) #s(literal 2 binary64)) (*.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/2 binary64) eps))))))
(/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(literal 1/2 binary64)) (neg.f64 eps))
(/.f64 (*.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/2 binary64)) (*.f64 eps eps))
(/.f64 (*.f64 #s(literal 1/2 binary64) (neg.f64 (*.f64 eps eps))) (neg.f64 eps))
(/.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 eps #s(literal 3 binary64))) (*.f64 eps eps))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 #s(literal 1/2 binary64) eps) #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/2 binary64) eps)))
(/.f64 (+.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/8 binary64) (pow.f64 eps #s(literal 3 binary64)))) (+.f64 #s(literal 0 binary64) (-.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) eps) #s(literal 2 binary64)) (*.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/2 binary64) eps)))))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 eps) (*.f64 (neg.f64 (*.f64 eps eps)) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps eps) (*.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 eps) (*.f64 #s(literal 1/2 binary64) (neg.f64 (*.f64 eps eps)))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps eps) (*.f64 #s(literal 1/2 binary64) (pow.f64 eps #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/2 binary64) eps)) (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 #s(literal 1/2 binary64) eps) #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 0 binary64) (-.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) eps) #s(literal 2 binary64)) (*.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/2 binary64) eps)))) (+.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/8 binary64) (pow.f64 eps #s(literal 3 binary64))))))
(/.f64 #s(literal 1/2 binary64) (pow.f64 eps #s(literal -1 binary64)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) eps) (/.f64 (pow.f64 eps #s(literal 3 binary64)) eps) #s(literal 0 binary64))
(fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) eps) (/.f64 #s(literal 1/2 binary64) eps) #s(literal 0 binary64))
(fma.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(literal 1/2 binary64)) (pow.f64 (neg.f64 eps) #s(literal -1 binary64)) #s(literal 0 binary64))
(fma.f64 (*.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/2 binary64)) (pow.f64 eps #s(literal -2 binary64)) #s(literal 0 binary64))
(fma.f64 (*.f64 #s(literal 1/2 binary64) (neg.f64 (*.f64 eps eps))) (pow.f64 (neg.f64 eps) #s(literal -1 binary64)) #s(literal 0 binary64))
(fma.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 eps #s(literal 3 binary64))) (pow.f64 eps #s(literal -2 binary64)) #s(literal 0 binary64))
(fma.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 #s(literal 1/2 binary64) eps) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 0 binary64))
(fma.f64 (+.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/8 binary64) (pow.f64 eps #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 0 binary64) (-.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) eps) #s(literal 2 binary64)) (*.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/2 binary64) eps))))) #s(literal 0 binary64))
(fma.f64 #s(literal 1/2 binary64) eps #s(literal 0 binary64))
(fma.f64 eps #s(literal 1/2 binary64) #s(literal 0 binary64))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/2 binary64) eps))) (/.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) eps) #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/2 binary64) eps))))
(+.f64 (*.f64 #s(literal 1/2 binary64) eps) #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/2 binary64) eps))
(sin.f64 x)

eval197.0ms (1.6%)

Memory
5.4MiB live, 286.0MiB allocated
Compiler

Compiled 28 662 to 3 084 computations (89.2% saved)

prune61.0ms (0.5%)

Memory
17.0MiB live, 93.6MiB allocated
Pruning

23 alts after pruning (19 fresh and 4 done)

PrunedKeptTotal
New1 128181 146
Fresh011
Picked235
Done011
Total1 130231 153
Accuracy
100.0%
Counts
1 153 → 23
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.8%
(fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (cos.f64 eps) (sin.f64 x) (neg.f64 (sin.f64 x))))
64.4%
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
34.8%
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (/.f64 #s(literal 1 binary64) (neg.f64 (*.f64 eps eps)))))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
99.2%
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64)) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
99.1%
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
98.9%
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
98.8%
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
98.9%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps))
98.5%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) x #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
98.5%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) eps))
98.5%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
98.5%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
98.3%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) x (*.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
98.1%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
98.0%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) eps))
98.2%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 eps x) #s(literal -1/2 binary64)) x (*.f64 eps #s(literal -1/2 binary64))) x #s(literal 1 binary64))) eps))
98.2%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
98.0%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 eps x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
98.1%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
98.3%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
98.2%
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
98.1%
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps x) eps)))
100.0%
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))))
Compiler

Compiled 630 to 491 computations (22.1% saved)

simplify145.0ms (1.2%)

Memory
10.6MiB live, 92.1MiB allocated
Algorithm
egg-herbie
Localize:

Found 19 expressions of interest:

NewMetricScoreProgram
cost-diff0
#s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) x #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps)))
cost-diff0
(fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) x #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x))
cost-diff0
(*.f64 (fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) x #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps)
cost-diff0
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) x #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
cost-diff0
#s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) x (*.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))
cost-diff0
(*.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) x (*.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps)
cost-diff0
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) x (*.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
cost-diff192
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) x (*.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))
cost-diff0
(fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))
cost-diff0
#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64)))
cost-diff0
(*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps)
cost-diff0
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
cost-diff0
#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))
cost-diff0
(*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)
cost-diff0
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
cost-diff0
(*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
cost-diff0
(*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))))
cost-diff0
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))))
cost-diff128
(cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))
Rules
10 932×lower-fma.f32
10 914×lower-fma.f64
3 028×lower-*.f32
3 004×lower-*.f64
1 880×lower-+.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
067545
0101543
1180543
2390543
3803543
41444543
51685543
61852543
72849543
84616541
96250541
107834541
08114517
Stop Event
iter limit
node limit
iter limit
Calls
Call 1
Inputs
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))))
(*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))))
(*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
#s(literal 2 binary64)
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 #s(literal 1/2 binary64) eps)
#s(literal 1/2 binary64)
eps
(cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))
(fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))
#s(literal -1/2 binary64)
(neg.f64 x)
x
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
(*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)
#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))
#s(literal 1 binary64)
eps
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
(*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps)
#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64)))
(fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))
(*.f64 (+.f64 eps x) #s(literal -1/2 binary64))
(+.f64 eps x)
eps
x
#s(literal -1/2 binary64)
#s(literal 1 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) x (*.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
(*.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) x (*.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps)
#s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) x (*.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) x (*.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))
(fma.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) x (*.f64 eps #s(literal -1/2 binary64)))
(fma.f64 #s(literal 1/12 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
#s(literal 1/12 binary64)
(*.f64 eps eps)
eps
#s(literal -1/2 binary64)
x
(*.f64 eps #s(literal -1/2 binary64))
(fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))
#s(literal -1/6 binary64)
#s(literal 1 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) x #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
(*.f64 (fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) x #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps)
(fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) x #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x))
#s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) x #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps)))
(fma.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) x #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))
(fma.f64 (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) x #s(literal -1/2 binary64))
(*.f64 #s(literal 1/12 binary64) (+.f64 eps x))
#s(literal 1/12 binary64)
(+.f64 eps x)
eps
x
#s(literal -1/2 binary64)
(*.f64 #s(literal -1/6 binary64) eps)
#s(literal -1/6 binary64)
(cos.f64 x)
Outputs
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))))
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(literal -2 binary64)) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))))
(*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))))
(*.f64 (*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(literal -2 binary64)) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)))
(*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) #s(literal -2 binary64))
#s(literal 2 binary64)
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(*.f64 #s(literal 1/2 binary64) eps)
(*.f64 eps #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
eps
(cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))
(fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))
#s(literal -1/2 binary64)
(neg.f64 x)
x
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
(*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)
#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))
#s(literal 1 binary64)
eps
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
(*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps)
(*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps)
#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64)))
#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64)))
(fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))
(fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))
(*.f64 (+.f64 eps x) #s(literal -1/2 binary64))
(*.f64 (+.f64 x eps) #s(literal -1/2 binary64))
(+.f64 eps x)
(+.f64 x eps)
eps
x
#s(literal -1/2 binary64)
#s(literal 1 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) x (*.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64)) (*.f64 eps eps) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64)))) eps))
(*.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) x (*.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps)
(*.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64)) (*.f64 eps eps) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64)))) eps)
#s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) x (*.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))
#s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64)) (*.f64 eps eps) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) x (*.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))
(fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64)) (*.f64 eps eps) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64)))
(fma.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) x (*.f64 eps #s(literal -1/2 binary64)))
(fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))
(fma.f64 #s(literal 1/12 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
(fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64))
#s(literal 1/12 binary64)
(*.f64 eps eps)
eps
#s(literal -1/2 binary64)
x
(*.f64 eps #s(literal -1/2 binary64))
(*.f64 #s(literal -1/2 binary64) eps)
(fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))
#s(literal -1/6 binary64)
#s(literal 1 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) x #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) (+.f64 x eps)) x #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
(*.f64 (fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) x #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps)
(*.f64 (fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) (+.f64 x eps)) x #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps)
(fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) x #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x))
(fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) (+.f64 x eps)) x #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x))
#s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) x #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps)))
#s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) (+.f64 x eps)) x #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps)))
(fma.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) x #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))
(fma.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) (+.f64 x eps)) x #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))
(fma.f64 (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) x #s(literal -1/2 binary64))
(fma.f64 (*.f64 #s(literal 1/12 binary64) (+.f64 x eps)) x #s(literal -1/2 binary64))
(*.f64 #s(literal 1/12 binary64) (+.f64 eps x))
(*.f64 #s(literal 1/12 binary64) (+.f64 x eps))
#s(literal 1/12 binary64)
(+.f64 eps x)
(+.f64 x eps)
eps
x
#s(literal -1/2 binary64)
(*.f64 #s(literal -1/6 binary64) eps)
#s(literal -1/6 binary64)
(cos.f64 x)

localize235.0ms (2%)

Memory
12.1MiB live, 242.5MiB allocated
Localize:

Found 19 expressions of interest:

NewMetricScoreProgram
accuracy0.28125
(*.f64 #s(literal -1/6 binary64) eps)
accuracy0.421875
(*.f64 #s(literal 1/12 binary64) (+.f64 eps x))
accuracy0.6894019019108873
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) x #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
accuracy1.0352378768990869
#s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) x #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps)))
accuracy0.015625
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) x (*.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))
accuracy0.015625
(fma.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) x (*.f64 eps #s(literal -1/2 binary64)))
accuracy0.6894019019108873
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) x (*.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
accuracy1.1322690651836185
#s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) x (*.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))
accuracy0
(*.f64 (+.f64 eps x) #s(literal -1/2 binary64))
accuracy0
(*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps)
accuracy0.7730052602805118
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
accuracy1.1064928042398687
#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64)))
accuracy0
(*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)
accuracy0.7730052602805118
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
accuracy1.2137897108165974
#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))
accuracy0
(neg.f64 x)
accuracy0
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))))
accuracy0.00390625
(*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))))
accuracy0.03142341452874396
(cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))
Samples
75.0ms171×0valid
57.0ms79×1valid
27.0ms5exit
2.0ms3valid
1.0ms2valid
Compiler

Compiled 340 to 63 computations (81.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 130.0ms
ival-mult: 68.0ms (52.3% of total)
ival-add: 23.0ms (17.7% of total)
adjust: 12.0ms (9.2% of total)
ival-sin: 8.0ms (6.2% of total)
const: 7.0ms (5.4% of total)
ival-cos: 6.0ms (4.6% of total)
ival-div: 2.0ms (1.5% of total)
ival-sub: 1.0ms (0.8% of total)
exact: 1.0ms (0.8% of total)
ival-neg: 1.0ms (0.8% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series76.0ms (0.6%)

Memory
-19.9MiB live, 80.4MiB allocated
Counts
24 → 540
Calls
Call 1
Inputs
#s(alt (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (patch (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) #<representation binary64>) () ())
#s(alt #s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))))) (patch #s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))))) #<representation binary64>) () ())
#s(alt (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))) (patch (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))) #<representation binary64>) () ())
#s(alt (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (patch (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #<representation binary64>) () ())
#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)) #<representation binary64>) () ())
#s(alt (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps) (patch (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) (patch #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps)) #<representation binary64>) () ())
#s(alt (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps) (patch (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) (patch #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64)) (patch (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) x (*.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) (patch (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) x (*.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) x (*.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) x (*.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps)) #<representation binary64>) () ())
#s(alt (*.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) x (*.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps) (patch (*.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) x (*.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) x (*.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) (patch #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) x (*.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) x #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) x #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps)) #<representation binary64>) () ())
#s(alt (*.f64 (fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) x #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps) (patch (*.f64 (fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) x #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps) #<representation binary64>) () ())
#s(alt (fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) x #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) (patch (fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) x #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) #<representation binary64>) () ())
#s(alt #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) x #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) (patch #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) x #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) #<representation binary64>) () ())
#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())
#s(alt (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) (patch (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) x (*.f64 eps #s(literal -1/2 binary64))) (patch (fma.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) x (*.f64 eps #s(literal -1/2 binary64))) #<representation binary64>) () ())
#s(alt (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) (patch (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) #<representation binary64>) () ())
#s(alt (*.f64 #s(literal -1/6 binary64) eps) (patch (*.f64 #s(literal -1/6 binary64) eps) #<representation binary64>) () ())
Outputs
#s(alt (cos (neg x)) (taylor 0 eps) (#s(alt (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (patch (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt (+ (cos (neg x)) (* 1/2 (* eps (sin (neg x))))) (taylor 0 eps) (#s(alt (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (patch (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt (+ (cos (neg x)) (* eps (- (* -1/8 (* eps (cos (neg x)))) (* -1/2 (sin (neg x)))))) (taylor 0 eps) (#s(alt (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (patch (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt (+ (cos (neg x)) (* eps (- (* eps (+ (* -1/8 (cos (neg x))) (* -1/48 (* eps (sin (neg x)))))) (* -1/2 (sin (neg x)))))) (taylor 0 eps) (#s(alt (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (patch (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* eps (cos (* -1 x))) (taylor 0 eps) (#s(alt #s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))))) (patch #s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))) (taylor 0 eps) (#s(alt #s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))))) (patch #s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))) (taylor 0 eps) (#s(alt #s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))))) (patch #s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))) (taylor 0 eps) (#s(alt #s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))))) (patch #s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))))) #<representation binary64>) () ())) ())
#s(alt (* eps (cos (neg x))) (taylor 0 eps) (#s(alt (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))) (patch (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos (neg x)) (* 1/2 (* eps (sin (neg x)))))) (taylor 0 eps) (#s(alt (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))) (patch (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos (neg x)) (* eps (+ (* 1/2 (sin (neg x))) (* 2 (* eps (+ (* -1/16 (cos (neg x))) (* -1/48 (cos (neg x)))))))))) (taylor 0 eps) (#s(alt (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))) (patch (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos (neg x)) (* eps (+ (* 1/2 (sin (neg x))) (* eps (+ (* -1/24 (* eps (sin (neg x)))) (* 2 (+ (* -1/16 (cos (neg x))) (* -1/48 (cos (neg x))))))))))) (taylor 0 eps) (#s(alt (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))) (patch (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 eps) (#s(alt (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (patch (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (* -1/24 (pow eps 2)))) (taylor 0 eps) (#s(alt (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (patch (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24)))) (taylor 0 eps) (#s(alt (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (patch (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24)))) (taylor 0 eps) (#s(alt (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (patch (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #<representation binary64>) () ())) ())
#s(alt (* eps (cos x)) (taylor 0 eps) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* -1/2 (* eps (sin x))))) (taylor 0 eps) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)) #<representation binary64>) () ())) ())
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#s(alt (* -1 (* x (+ (* -1 (- (* 1/12 (pow eps 2)) 1/2)) (* 1/2 (/ eps x))))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) x (*.f64 eps #s(literal -1/2 binary64))) (patch (fma.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) x (*.f64 eps #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
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#s(alt (* 1/12 x) (taylor -inf x) (#s(alt (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) (patch (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/12 (/ eps x)) 1/12))) (taylor -inf x) (#s(alt (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) (patch (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/12 (/ eps x)) 1/12))) (taylor -inf x) (#s(alt (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) (patch (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/12 (/ eps x)) 1/12))) (taylor -inf x) (#s(alt (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) (patch (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) #<representation binary64>) () ())) ())
Calls

6 calls:

TimeVariablePointExpression
27.0ms
eps
@0
((cos (+ (* eps -1/2) (neg x))) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (* 2 (sin (* 1/2 eps))) (cos (+ (* eps -1/2) (neg x)))) (* 2 (sin (* 1/2 eps))) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (+ (* (* (+ eps x) -1/2) x) 1) (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* eps -1/2)) x) (+ (* (* eps eps) -1/6) 1)) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (neg x) (* (+ eps x) -1/2) (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* eps -1/2)) (* 1/12 (+ eps x)) (* -1/6 eps))
6.0ms
x
@0
((cos (+ (* eps -1/2) (neg x))) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (* 2 (sin (* 1/2 eps))) (cos (+ (* eps -1/2) (neg x)))) (* 2 (sin (* 1/2 eps))) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (+ (* (* (+ eps x) -1/2) x) 1) (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* eps -1/2)) x) (+ (* (* eps eps) -1/6) 1)) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (neg x) (* (+ eps x) -1/2) (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* eps -1/2)) (* 1/12 (+ eps x)) (* -1/6 eps))
4.0ms
eps
@inf
((cos (+ (* eps -1/2) (neg x))) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (* 2 (sin (* 1/2 eps))) (cos (+ (* eps -1/2) (neg x)))) (* 2 (sin (* 1/2 eps))) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (+ (* (* (+ eps x) -1/2) x) 1) (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* eps -1/2)) x) (+ (* (* eps eps) -1/6) 1)) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (neg x) (* (+ eps x) -1/2) (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* eps -1/2)) (* 1/12 (+ eps x)) (* -1/6 eps))
4.0ms
x
@inf
((cos (+ (* eps -1/2) (neg x))) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (* 2 (sin (* 1/2 eps))) (cos (+ (* eps -1/2) (neg x)))) (* 2 (sin (* 1/2 eps))) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (+ (* (* (+ eps x) -1/2) x) 1) (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* eps -1/2)) x) (+ (* (* eps eps) -1/6) 1)) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (neg x) (* (+ eps x) -1/2) (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* eps -1/2)) (* 1/12 (+ eps x)) (* -1/6 eps))
4.0ms
x
@-inf
((cos (+ (* eps -1/2) (neg x))) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (* 2 (sin (* 1/2 eps))) (cos (+ (* eps -1/2) (neg x)))) (* 2 (sin (* 1/2 eps))) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (+ (* (* (+ eps x) -1/2) x) 1) (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* eps -1/2)) x) (+ (* (* eps eps) -1/6) 1)) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (neg x) (* (+ eps x) -1/2) (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* eps -1/2)) (* 1/12 (+ eps x)) (* -1/6 eps))

simplify251.0ms (2.1%)

Memory
3.9MiB live, 346.6MiB allocated
Algorithm
egg-herbie
Rules
15 972×lower-fma.f64
15 972×lower-fma.f32
6 486×lower-*.f64
6 486×lower-*.f32
4 238×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04526425
114376180
237555990
084295450
Stop Event
iter limit
node limit
Counts
540 → 537
Calls
Call 1
Inputs
(cos (neg x))
(+ (cos (neg x)) (* 1/2 (* eps (sin (neg x)))))
(+ (cos (neg x)) (* eps (- (* -1/8 (* eps (cos (neg x)))) (* -1/2 (sin (neg x))))))
(+ (cos (neg x)) (* eps (- (* eps (+ (* -1/8 (cos (neg x))) (* -1/48 (* eps (sin (neg x)))))) (* -1/2 (sin (neg x))))))
(* eps (cos (* -1 x)))
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))))
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))))
(* eps (cos (neg x)))
(* eps (+ (cos (neg x)) (* 1/2 (* eps (sin (neg x))))))
(* eps (+ (cos (neg x)) (* eps (+ (* 1/2 (sin (neg x))) (* 2 (* eps (+ (* -1/16 (cos (neg x))) (* -1/48 (cos (neg x))))))))))
(* eps (+ (cos (neg x)) (* eps (+ (* 1/2 (sin (neg x))) (* eps (+ (* -1/24 (* eps (sin (neg x)))) (* 2 (+ (* -1/16 (cos (neg x))) (* -1/48 (cos (neg x)))))))))))
eps
(* eps (+ 1 (* -1/24 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))
(+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6))))))
(+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6))))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(* -1/2 (sin x))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(* -1/2 x)
(+ (* -1/2 eps) (* -1/2 x))
(+ (* -1/2 eps) (* -1/2 x))
(+ (* -1/2 eps) (* -1/2 x))
(* -1/2 x)
(+ (* -1/2 eps) (* -1/2 x))
(+ (* -1/2 x) (* eps (- (* 1/12 (* eps x)) 1/2)))
(+ (* -1/2 x) (* eps (- (* 1/12 (* eps x)) 1/2)))
(* 1/12 x)
(+ (* 1/12 eps) (* 1/12 x))
(+ (* 1/12 eps) (* 1/12 x))
(+ (* 1/12 eps) (* 1/12 x))
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(cos (neg (+ x (* 1/2 eps))))
(cos (neg (+ x (* 1/2 eps))))
(cos (neg (+ x (* 1/2 eps))))
(cos (neg (+ x (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (neg (+ x (* 1/2 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (neg (+ x (* 1/2 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (neg (+ x (* 1/2 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (neg (+ x (* 1/2 eps)))) (sin (* 1/2 eps))))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps (sin x)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps (sin x)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps x))
(* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))
(* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6))
(* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/12 (pow x 2)) (/ 1 (pow eps 2))))) 1/6))
(* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/12 (pow x 2)) (/ 1 (pow eps 2))))) 1/6))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* -1/6 (* (pow eps 3) (cos x)))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* -1/6 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* -1/6 (* (pow eps 3) (cos x)))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* -1/6 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* -1/6 (* eps (cos x)))
(* eps (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* eps (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* eps (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* -1/2 eps)
(* eps (- (* -1/2 (/ x eps)) 1/2))
(* eps (- (* -1/2 (/ x eps)) 1/2))
(* eps (- (* -1/2 (/ x eps)) 1/2))
(* 1/12 (* (pow eps 2) x))
(* (pow eps 2) (- (* 1/12 x) (* 1/2 (/ 1 eps))))
(* (pow eps 2) (- (+ (* -1/2 (/ x (pow eps 2))) (* 1/12 x)) (* 1/2 (/ 1 eps))))
(* (pow eps 2) (- (+ (* -1/2 (/ x (pow eps 2))) (* 1/12 x)) (* 1/2 (/ 1 eps))))
(* 1/12 eps)
(* eps (+ 1/12 (* 1/12 (/ x eps))))
(* eps (+ 1/12 (* 1/12 (/ x eps))))
(* eps (+ 1/12 (* 1/12 (/ x eps))))
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(cos (- (* -1/2 eps) x))
(cos (- (* -1/2 eps) x))
(cos (- (* -1/2 eps) x))
(cos (- (* -1/2 eps) x))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (- (* -1/2 eps) x)) (sin (* 1/2 eps))))
(* 2 (* (cos (- (* -1/2 eps) x)) (sin (* 1/2 eps))))
(* 2 (* (cos (- (* -1/2 eps) x)) (sin (* 1/2 eps))))
(* 2 (* (cos (- (* -1/2 eps) x)) (sin (* 1/2 eps))))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps (sin x)))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps (sin x)))
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(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1/2 (* eps x))
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(* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x))))
(* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x))))
(* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))
(* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6))
(* (pow eps 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x)) eps)) (* 1/12 (pow x 2))) 1/6))
(* (pow eps 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x)) eps)) (* 1/12 (pow x 2))) 1/6))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(* -1/6 (* (pow eps 3) (cos x)))
(* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))
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(* -1/6 (* (pow eps 2) (cos x)))
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(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(* -1/6 (* (pow eps 3) (cos x)))
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(* -1/6 (* (pow eps 2) (cos x)))
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(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))
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(* -1/6 (* eps (cos x)))
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(* -1 (* eps (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))
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(* -1/2 eps)
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(* -1 (* eps (+ 1/2 (* 1/2 (/ x eps)))))
(* -1 (* eps (+ 1/2 (* 1/2 (/ x eps)))))
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(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(cos (* -1/2 eps))
(+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps))))
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(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))
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(sin eps)
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(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
eps
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(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
1
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(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
1
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(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
1
(+ 1 (* -1/2 (* eps x)))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
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(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2))))))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* 1/12 (* (pow eps 2) x)) (* eps (- (* 1/12 (pow eps 2)) 1/2)))))))
(+ 1 (* -1/6 (pow eps 2)))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2))))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2))))))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* 1/12 (* (pow eps 2) x)) (* eps (- (* 1/12 (pow eps 2)) 1/2)))))))
(+ 1 (* -1/6 (pow eps 2)))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2))))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2))))))
(* -1/6 eps)
(+ (* -1/2 x) (* -1/6 eps))
(+ (* -1/6 eps) (* x (- (* 1/12 (* eps x)) 1/2)))
(+ (* -1/6 eps) (* x (- (* x (+ (* 1/12 eps) (* 1/12 x))) 1/2)))
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1/2 eps)
(+ (* -1/2 eps) (* -1/2 x))
(+ (* -1/2 eps) (* -1/2 x))
(+ (* -1/2 eps) (* -1/2 x))
(* -1/2 eps)
(+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2)))
(+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2)))
(+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2)))
(* 1/12 eps)
(+ (* 1/12 eps) (* 1/12 x))
(+ (* 1/12 eps) (* 1/12 x))
(+ (* 1/12 eps) (* 1/12 x))
(cos (- (* -1/2 eps) x))
(cos (- (* -1/2 eps) x))
(cos (- (* -1/2 eps) x))
(cos (- (* -1/2 eps) x))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (- (* -1/2 eps) x)) (sin (* 1/2 eps))))
(* 2 (* (cos (- (* -1/2 eps) x)) (sin (* 1/2 eps))))
(* 2 (* (cos (- (* -1/2 eps) x)) (sin (* 1/2 eps))))
(* 2 (* (cos (- (* -1/2 eps) x)) (sin (* 1/2 eps))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* -1/2 (pow x 2))
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (/ 1 (pow x 2))) 1/2))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (/ 1 (pow x 2))) 1/2))
(* (pow x 2) (- (* 1/12 (pow eps 2)) 1/2))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (+ (* -1/6 (/ (pow eps 2) (pow x 2))) (+ (* 1/12 (pow eps 2)) (/ 1 (pow x 2))))) 1/2))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (+ (* -1/6 (/ (pow eps 2) (pow x 2))) (+ (* 1/12 (pow eps 2)) (/ 1 (pow x 2))))) 1/2))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1/2 x)
(* x (- (* -1/2 (/ eps x)) 1/2))
(* x (- (* -1/2 (/ eps x)) 1/2))
(* x (- (* -1/2 (/ eps x)) 1/2))
(* x (- (* 1/12 (pow eps 2)) 1/2))
(* x (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))
(* x (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))
(* x (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))
(* 1/12 x)
(* x (+ 1/12 (* 1/12 (/ eps x))))
(* x (+ 1/12 (* 1/12 (/ eps x))))
(* x (+ 1/12 (* 1/12 (/ eps x))))
(cos (+ (* -1 x) (* -1/2 eps)))
(cos (+ (* -1 x) (* -1/2 eps)))
(cos (+ (* -1 x) (* -1/2 eps)))
(cos (+ (* -1 x) (* -1/2 eps)))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (+ (* -1 x) (* -1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (+ (* -1 x) (* -1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (+ (* -1 x) (* -1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (+ (* -1 x) (* -1/2 eps))) (sin (* 1/2 eps))))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* -1/2 (pow x 2))
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))
(* (pow x 2) (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2))
(* (pow x 2) (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2))
(* (pow x 2) (- (* 1/12 (pow eps 2)) 1/2))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))
(* (pow x 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/6 (pow eps 2))) x)) (* 1/2 eps)) x)) (* 1/12 (pow eps 2))) 1/2))
(* (pow x 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/6 (pow eps 2))) x)) (* 1/2 eps)) x)) (* 1/12 (pow eps 2))) 1/2))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1/2 x)
(* -1 (* x (+ 1/2 (* 1/2 (/ eps x)))))
(* -1 (* x (+ 1/2 (* 1/2 (/ eps x)))))
(* -1 (* x (+ 1/2 (* 1/2 (/ eps x)))))
(* x (- (* 1/12 (pow eps 2)) 1/2))
(* -1 (* x (+ (* -1 (- (* 1/12 (pow eps 2)) 1/2)) (* 1/2 (/ eps x)))))
(* -1 (* x (+ (* -1 (- (* 1/12 (pow eps 2)) 1/2)) (* 1/2 (/ eps x)))))
(* -1 (* x (+ (* -1 (- (* 1/12 (pow eps 2)) 1/2)) (* 1/2 (/ eps x)))))
(* 1/12 x)
(* -1 (* x (- (* -1/12 (/ eps x)) 1/12)))
(* -1 (* x (- (* -1/12 (/ eps x)) 1/12)))
(* -1 (* x (- (* -1/12 (/ eps x)) 1/12)))
Outputs
(cos (neg x))
(cos.f64 x)
(+ (cos (neg x)) (* 1/2 (* eps (sin (neg x)))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) eps) (sin.f64 x) (cos.f64 x))
(+ (cos (neg x)) (* eps (- (* -1/8 (* eps (cos (neg x)))) (* -1/2 (sin (neg x))))))
(fma.f64 (fma.f64 (sin.f64 x) #s(literal -1/2 binary64) (*.f64 (*.f64 #s(literal -1/8 binary64) eps) (cos.f64 x))) eps (cos.f64 x))
(+ (cos (neg x)) (* eps (- (* eps (+ (* -1/8 (cos (neg x))) (* -1/48 (* eps (sin (neg x)))))) (* -1/2 (sin (neg x))))))
(fma.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) eps) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 x)) (fma.f64 eps (*.f64 #s(literal -1/48 binary64) eps) #s(literal 1/2 binary64)))) eps (cos.f64 x))
(* eps (cos (* -1 x)))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))))
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) (sin.f64 x) (cos.f64 x)) eps)
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))
(*.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal -1/2 binary64) (*.f64 (*.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) eps)
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))))
(*.f64 (fma.f64 (fma.f64 (neg.f64 (sin.f64 x)) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/24 binary64))) (*.f64 (*.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) eps)
(* eps (cos (neg x)))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos (neg x)) (* 1/2 (* eps (sin (neg x))))))
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) (sin.f64 x) (cos.f64 x)) eps)
(* eps (+ (cos (neg x)) (* eps (+ (* 1/2 (sin (neg x))) (* 2 (* eps (+ (* -1/16 (cos (neg x))) (* -1/48 (cos (neg x))))))))))
(*.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal -1/2 binary64) (*.f64 (*.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) eps)
(* eps (+ (cos (neg x)) (* eps (+ (* 1/2 (sin (neg x))) (* eps (+ (* -1/24 (* eps (sin (neg x)))) (* 2 (+ (* -1/16 (cos (neg x))) (* -1/48 (cos (neg x)))))))))))
(*.f64 (fma.f64 (fma.f64 (neg.f64 (sin.f64 x)) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/24 binary64))) (*.f64 (*.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) eps)
eps
(* eps (+ 1 (* -1/24 (pow eps 2))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/24 binary64) eps)
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 1/1920 binary64) (*.f64 eps eps) #s(literal -1/24 binary64)) eps)
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps) #s(literal -1/24 binary64)) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) (sin.f64 x) (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(*.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal -1/2 binary64) (*.f64 (*.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 (sin.f64 x) (fma.f64 eps (*.f64 #s(literal 1/24 binary64) eps) #s(literal -1/2 binary64)))) eps (cos.f64 x)) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) (sin.f64 x) (cos.f64 x)) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) (sin.f64 x) (cos.f64 x)) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) (sin.f64 x) (cos.f64 x)) eps)
(cos x)
(cos.f64 x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) eps) (sin.f64 x) (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) eps) (sin.f64 x) (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) eps) (sin.f64 x) (cos.f64 x))
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) (sin.f64 x) (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(*.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal -1/2 binary64) (*.f64 (*.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 (sin.f64 x) (fma.f64 eps (*.f64 #s(literal 1/24 binary64) eps) #s(literal -1/2 binary64)))) eps (cos.f64 x)) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) (sin.f64 x) (cos.f64 x)) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) (sin.f64 x) (cos.f64 x)) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) (sin.f64 x) (cos.f64 x)) eps)
(cos x)
(cos.f64 x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) eps) (sin.f64 x) (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) eps) (sin.f64 x) (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) eps) (sin.f64 x) (cos.f64 x))
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))
(fma.f64 (*.f64 x (+.f64 eps x)) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))
(fma.f64 (*.f64 x (+.f64 eps x)) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))
(fma.f64 (*.f64 x (+.f64 eps x)) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))
(fma.f64 (*.f64 x (+.f64 eps x)) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 x x) #s(literal -1/6 binary64)) eps (*.f64 #s(literal -1/2 binary64) x)) eps (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
(+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 x x) #s(literal -1/6 binary64)) eps (*.f64 #s(literal -1/2 binary64) x)) eps (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) (sin.f64 x) (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(*.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal -1/2 binary64) (*.f64 (*.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 (sin.f64 x) (fma.f64 eps (*.f64 #s(literal 1/24 binary64) eps) #s(literal -1/2 binary64)))) eps (cos.f64 x)) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) (sin.f64 x) (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(*.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal -1/2 binary64) (*.f64 (*.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(*.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal -1/2 binary64) (*.f64 (*.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) eps)
(cos x)
(cos.f64 x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) eps) (sin.f64 x) (cos.f64 x))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(fma.f64 (fma.f64 (sin.f64 x) #s(literal -1/2 binary64) (*.f64 (*.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(fma.f64 (fma.f64 (sin.f64 x) #s(literal -1/2 binary64) (*.f64 (*.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x))
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) (sin.f64 x) (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(*.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal -1/2 binary64) (*.f64 (*.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 (sin.f64 x) (fma.f64 eps (*.f64 #s(literal 1/24 binary64) eps) #s(literal -1/2 binary64)))) eps (cos.f64 x)) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) (sin.f64 x) (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(*.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal -1/2 binary64) (*.f64 (*.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(*.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal -1/2 binary64) (*.f64 (*.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) eps)
(cos x)
(cos.f64 x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) eps) (sin.f64 x) (cos.f64 x))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(fma.f64 (fma.f64 (sin.f64 x) #s(literal -1/2 binary64) (*.f64 (*.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(fma.f64 (fma.f64 (sin.f64 x) #s(literal -1/2 binary64) (*.f64 (*.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x))
(* -1/2 (sin x))
(*.f64 (sin.f64 x) #s(literal -1/2 binary64))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(fma.f64 (sin.f64 x) #s(literal -1/2 binary64) (*.f64 (*.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(fma.f64 (sin.f64 x) #s(literal -1/2 binary64) (*.f64 (*.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(fma.f64 (sin.f64 x) #s(literal -1/2 binary64) (*.f64 (*.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps))
(* -1/2 x)
(*.f64 #s(literal -1/2 binary64) x)
(+ (* -1/2 eps) (* -1/2 x))
(*.f64 (+.f64 eps x) #s(literal -1/2 binary64))
(+ (* -1/2 eps) (* -1/2 x))
(*.f64 (+.f64 eps x) #s(literal -1/2 binary64))
(+ (* -1/2 eps) (* -1/2 x))
(*.f64 (+.f64 eps x) #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 #s(literal -1/2 binary64) x)
(+ (* -1/2 eps) (* -1/2 x))
(*.f64 (+.f64 eps x) #s(literal -1/2 binary64))
(+ (* -1/2 x) (* eps (- (* 1/12 (* eps x)) 1/2)))
(fma.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) eps) eps #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))
(+ (* -1/2 x) (* eps (- (* 1/12 (* eps x)) 1/2)))
(fma.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) eps) eps #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))
(* 1/12 x)
(*.f64 #s(literal 1/12 binary64) x)
(+ (* 1/12 eps) (* 1/12 x))
(*.f64 (+.f64 eps x) #s(literal 1/12 binary64))
(+ (* 1/12 eps) (* 1/12 x))
(*.f64 (+.f64 eps x) #s(literal 1/12 binary64))
(+ (* 1/12 eps) (* 1/12 x))
(*.f64 (+.f64 eps x) #s(literal 1/12 binary64))
(* -1/6 eps)
(*.f64 #s(literal -1/6 binary64) eps)
(* -1/6 eps)
(*.f64 #s(literal -1/6 binary64) eps)
(* -1/6 eps)
(*.f64 #s(literal -1/6 binary64) eps)
(* -1/6 eps)
(*.f64 #s(literal -1/6 binary64) eps)
(cos (neg (+ x (* 1/2 eps))))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(cos (neg (+ x (* 1/2 eps))))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(cos (neg (+ x (* 1/2 eps))))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(cos (neg (+ x (* 1/2 eps))))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 2 (* (cos (neg (+ x (* 1/2 eps)))) (sin (* 1/2 eps))))
(*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 2 (* (cos (neg (+ x (* 1/2 eps)))) (sin (* 1/2 eps))))
(*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 2 (* (cos (neg (+ x (* 1/2 eps)))) (sin (* 1/2 eps))))
(*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 2 (* (cos (neg (+ x (* 1/2 eps)))) (sin (* 1/2 eps))))
(*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
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(*.f64 (fma.f64 eps (fma.f64 #s(literal 1/12 binary64) eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal -1/2 binary64)) x)
(* -1 (* x (+ (* -1 (- (* 1/12 (pow eps 2)) 1/2)) (* 1/2 (/ eps x)))))
(*.f64 (fma.f64 eps (fma.f64 #s(literal 1/12 binary64) eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal -1/2 binary64)) x)
(* -1 (* x (+ (* -1 (- (* 1/12 (pow eps 2)) 1/2)) (* 1/2 (/ eps x)))))
(*.f64 (fma.f64 eps (fma.f64 #s(literal 1/12 binary64) eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal -1/2 binary64)) x)
(* 1/12 x)
(*.f64 #s(literal 1/12 binary64) x)
(* -1 (* x (- (* -1/12 (/ eps x)) 1/12)))
(*.f64 (fma.f64 (/.f64 eps x) #s(literal 1/12 binary64) #s(literal 1/12 binary64)) x)
(* -1 (* x (- (* -1/12 (/ eps x)) 1/12)))
(*.f64 (fma.f64 (/.f64 eps x) #s(literal 1/12 binary64) #s(literal 1/12 binary64)) x)
(* -1 (* x (- (* -1/12 (/ eps x)) 1/12)))
(*.f64 (fma.f64 (/.f64 eps x) #s(literal 1/12 binary64) #s(literal 1/12 binary64)) x)

rewrite197.0ms (1.6%)

Memory
28.3MiB live, 214.2MiB allocated
Rules
5 884×lower-*.f32
5 860×lower-*.f64
5 374×lower-fma.f32
5 356×lower-fma.f64
2 988×lower-/.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
067464
0101462
1398462
23339462
08724445
Stop Event
iter limit
node limit
iter limit
Counts
24 → 363
Calls
Call 1
Inputs
(cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))))
(*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))))
(*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
(*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)
#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
(*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps)
#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64)))
(fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) x (*.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) x (*.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
(*.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) x (*.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps)
#s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) x (*.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) x #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
(*.f64 (fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) x #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps)
(fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) x #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x))
#s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) x #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps)))
(neg.f64 x)
(*.f64 (+.f64 eps x) #s(literal -1/2 binary64))
(fma.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) x (*.f64 eps #s(literal -1/2 binary64)))
(*.f64 #s(literal 1/12 binary64) (+.f64 eps x))
(*.f64 #s(literal -1/6 binary64) eps)
Outputs
(/.f64 (-.f64 (+.f64 (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (*.f64 #s(literal 1 binary64) x)))) (-.f64 (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (*.f64 #s(literal 1 binary64) x))) (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))))) #s(literal 2 binary64))
(/.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) (cos.f64 x)) #s(literal 2 binary64)) (pow.f64 (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) #s(literal 2 binary64))) (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (*.f64 #s(literal 1 binary64) x))))
(/.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) (cos.f64 x)) #s(literal 2 binary64)) (+.f64 (pow.f64 (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) #s(literal 2 binary64)) (*.f64 (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) (cos.f64 x)) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)))))))
(fma.f64 (cos.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps)) (fma.f64 #s(literal -1/2 binary64) eps (*.f64 #s(literal 1 binary64) x)))) (cos.f64 (/.f64 (*.f64 x x) (fma.f64 #s(literal -1/2 binary64) eps (*.f64 #s(literal 1 binary64) x)))) (*.f64 (sin.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps)) (fma.f64 #s(literal -1/2 binary64) eps (*.f64 #s(literal 1 binary64) x)))) (sin.f64 (/.f64 (*.f64 x x) (fma.f64 #s(literal -1/2 binary64) eps (*.f64 #s(literal 1 binary64) x))))))
(fma.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) (neg.f64 (sin.f64 x))))
(fma.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) (cos.f64 x) (neg.f64 (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)))))
(fma.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) (cos.f64 x) (*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x)))
(fma.f64 #s(literal 1 binary64) (cos.f64 (-.f64 x (*.f64 #s(literal -1/2 binary64) eps))) (*.f64 #s(literal 0 binary64) (sin.f64 (-.f64 x (*.f64 #s(literal -1/2 binary64) eps)))))
(fma.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 (neg.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) (neg.f64 (sin.f64 x))))
(fma.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) (neg.f64 (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)))))
(fma.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x)))
(-.f64 (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) (cos.f64 x)) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))))
(cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))
(+.f64 (*.f64 (cos.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps)) (fma.f64 #s(literal -1/2 binary64) eps (*.f64 #s(literal 1 binary64) x)))) (cos.f64 (/.f64 (*.f64 x x) (fma.f64 #s(literal -1/2 binary64) eps (*.f64 #s(literal 1 binary64) x))))) (*.f64 (sin.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps)) (fma.f64 #s(literal -1/2 binary64) eps (*.f64 #s(literal 1 binary64) x)))) (sin.f64 (/.f64 (*.f64 x x) (fma.f64 #s(literal -1/2 binary64) eps (*.f64 #s(literal 1 binary64) x))))))
(+.f64 (*.f64 #s(literal 1 binary64) (cos.f64 (-.f64 x (*.f64 #s(literal -1/2 binary64) eps)))) (*.f64 #s(literal 0 binary64) (sin.f64 (-.f64 x (*.f64 #s(literal -1/2 binary64) eps)))))
(+.f64 (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) (cos.f64 x)) (*.f64 (neg.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) (neg.f64 (sin.f64 x))))
(+.f64 (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) (cos.f64 x)) (neg.f64 (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)))))
(+.f64 (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) (cos.f64 x)) (*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x)))
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))))
(*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) #s(literal 2 binary64))
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))))
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))))
(*.f64 (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
(*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)
(*.f64 eps #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)))
(/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))) (neg.f64 eps))
(/.f64 (*.f64 (pow.f64 eps #s(literal 3 binary64)) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))) (*.f64 eps eps))
(/.f64 (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) (neg.f64 (*.f64 eps eps))) (neg.f64 eps))
(/.f64 (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) (pow.f64 eps #s(literal 3 binary64))) (*.f64 eps eps))
(fma.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) #s(literal 0 binary64) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
(fma.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps (*.f64 #s(literal 0 binary64) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))))
(fma.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) #s(literal 0 binary64)))
(fma.f64 #s(literal 0 binary64) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
(fma.f64 eps #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) (*.f64 #s(literal 0 binary64) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))))
(fma.f64 eps #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) #s(literal 0 binary64)))
(+.f64 (*.f64 #s(literal 0 binary64) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
(+.f64 (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) #s(literal 0 binary64)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
(+.f64 (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps) (*.f64 #s(literal 0 binary64) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))))
(+.f64 (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) #s(literal 0 binary64)))
#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
(*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps)
(*.f64 eps #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))))
(/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64)))) (neg.f64 eps))
(/.f64 (*.f64 (pow.f64 eps #s(literal 3 binary64)) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64)))) (*.f64 eps eps))
(/.f64 (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) (neg.f64 (*.f64 eps eps))) (neg.f64 eps))
(/.f64 (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) (pow.f64 eps #s(literal 3 binary64))) (*.f64 eps eps))
(fma.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) #s(literal 0 binary64) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
(fma.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps (*.f64 #s(literal 0 binary64) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64)))))
(fma.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) #s(literal 0 binary64)))
(fma.f64 #s(literal 0 binary64) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
(fma.f64 eps #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) (*.f64 #s(literal 0 binary64) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64)))))
(fma.f64 eps #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) #s(literal 0 binary64)))
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(/.f64 (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps)) (pow.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x) #s(literal 2 binary64))) (-.f64 (*.f64 #s(literal -1/2 binary64) eps) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x)))
(/.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x) #s(literal 2 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps)))) (neg.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (*.f64 #s(literal 1/2 binary64) eps))))
(/.f64 (neg.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 eps #s(literal 3 binary64)) (pow.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) (-.f64 (*.f64 #s(literal -1/2 binary64) eps) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x)) (pow.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x) #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x) #s(literal 2 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (*.f64 #s(literal 1/2 binary64) eps)))
(/.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 eps #s(literal 3 binary64)) (pow.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x) #s(literal 3 binary64))) (fma.f64 #s(literal 1/4 binary64) (*.f64 eps eps) (-.f64 (pow.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x) #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x) #s(literal -1/2 binary64)) eps))))
(/.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 eps #s(literal 3 binary64)) (pow.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x) #s(literal 3 binary64))) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) (-.f64 (*.f64 #s(literal -1/2 binary64) eps) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x)) (pow.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (*.f64 #s(literal 1/2 binary64) eps)) (-.f64 (pow.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x) #s(literal 2 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) (-.f64 (*.f64 #s(literal -1/2 binary64) eps) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x)) (pow.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/8 binary64) (pow.f64 eps #s(literal 3 binary64)) (pow.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x) #s(literal 3 binary64)))))
(fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))
(fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (*.f64 #s(literal -1/2 binary64) eps))
(fma.f64 #s(literal -1/2 binary64) eps (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x))
(fma.f64 eps #s(literal -1/2 binary64) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x))
(-.f64 (/.f64 (pow.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x) #s(literal 2 binary64)) (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (*.f64 #s(literal 1/2 binary64) eps))) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps)) (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (*.f64 #s(literal 1/2 binary64) eps))))
(+.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x) (*.f64 #s(literal -1/2 binary64) eps))
(+.f64 (*.f64 #s(literal -1/2 binary64) eps) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x))
(*.f64 #s(literal 1/12 binary64) (+.f64 x eps))
(*.f64 (+.f64 x eps) #s(literal 1/12 binary64))
(/.f64 (*.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) #s(literal 1/12 binary64)) (-.f64 x eps))
(/.f64 (*.f64 (*.f64 (+.f64 x eps) (-.f64 eps x)) #s(literal 1/12 binary64)) (-.f64 eps x))
(/.f64 (*.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) #s(literal 1/12 binary64)) (fma.f64 eps (-.f64 eps x) (*.f64 x x)))
(/.f64 (*.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) #s(literal 1/12 binary64)) (fma.f64 x (-.f64 x eps) (*.f64 eps eps)))
(/.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 (+.f64 x eps) (-.f64 x eps))) (-.f64 x eps))
(/.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 (+.f64 x eps) (-.f64 eps x))) (-.f64 eps x))
(/.f64 (*.f64 #s(literal 1/12 binary64) (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (fma.f64 eps (-.f64 eps x) (*.f64 x x)))
(/.f64 (*.f64 #s(literal 1/12 binary64) (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (fma.f64 x (-.f64 x eps) (*.f64 eps eps)))
(/.f64 (-.f64 (pow.f64 (*.f64 #s(literal 1/12 binary64) eps) #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal 1/12 binary64) x) #s(literal 2 binary64))) (-.f64 (*.f64 #s(literal 1/12 binary64) eps) (*.f64 #s(literal 1/12 binary64) x)))
(/.f64 (fma.f64 #s(literal 1/1728 binary64) (pow.f64 eps #s(literal 3 binary64)) (*.f64 #s(literal 1/1728 binary64) (pow.f64 x #s(literal 3 binary64)))) (+.f64 (pow.f64 (*.f64 #s(literal 1/12 binary64) eps) #s(literal 2 binary64)) (-.f64 (pow.f64 (*.f64 #s(literal 1/12 binary64) x) #s(literal 2 binary64)) (*.f64 (*.f64 #s(literal 1/12 binary64) eps) (*.f64 #s(literal 1/12 binary64) x)))))
(fma.f64 #s(literal 1/12 binary64) x (*.f64 #s(literal 1/12 binary64) eps))
(fma.f64 #s(literal 1/12 binary64) eps (*.f64 #s(literal 1/12 binary64) x))
(fma.f64 x #s(literal 1/12 binary64) (*.f64 #s(literal 1/12 binary64) eps))
(fma.f64 eps #s(literal 1/12 binary64) (*.f64 #s(literal 1/12 binary64) x))
(+.f64 (*.f64 #s(literal 1/12 binary64) x) (*.f64 #s(literal 1/12 binary64) eps))
(+.f64 (*.f64 #s(literal 1/12 binary64) eps) (*.f64 #s(literal 1/12 binary64) x))
(*.f64 #s(literal -1/6 binary64) eps)
(*.f64 eps #s(literal -1/6 binary64))
(/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(literal -1/6 binary64)) (neg.f64 eps))
(/.f64 (*.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64)) (*.f64 eps eps))
(/.f64 (*.f64 #s(literal -1/6 binary64) (neg.f64 (*.f64 eps eps))) (neg.f64 eps))
(/.f64 (*.f64 #s(literal -1/6 binary64) (pow.f64 eps #s(literal 3 binary64))) (*.f64 eps eps))
(fma.f64 #s(literal -1/6 binary64) eps #s(literal 0 binary64))
(fma.f64 eps #s(literal -1/6 binary64) #s(literal 0 binary64))
(+.f64 (*.f64 #s(literal -1/6 binary64) eps) #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/6 binary64) eps))

eval143.0ms (1.2%)

Memory
-36.7MiB live, 214.7MiB allocated
Compiler

Compiled 23 824 to 2 478 computations (89.6% saved)

prune39.0ms (0.3%)

Memory
20.2MiB live, 97.2MiB allocated
Pruning

29 alts after pruning (21 fresh and 8 done)

PrunedKeptTotal
New8919900
Fresh21214
Picked145
Done044
Total89429923
Accuracy
100.0%
Counts
923 → 29
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.8%
(fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (cos.f64 eps) (sin.f64 x) (neg.f64 (sin.f64 x))))
64.4%
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
34.8%
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (/.f64 #s(literal 1 binary64) (neg.f64 (*.f64 eps eps)))))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
99.2%
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64)) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
99.1%
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
98.9%
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
98.8%
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
53.3%
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64))))) (neg.f64 eps)))
53.1%
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))) (neg.f64 eps)))
98.9%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps))
98.5%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) x #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
98.5%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 (fma.f64 #s(approx (* 1/12 (+ eps x)) (*.f64 #s(literal 1/12 binary64) x)) x #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
98.5%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) eps))
98.5%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
98.5%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
98.3%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) x (*.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
98.1%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))) eps))
98.3%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 #s(approx (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* eps -1/2)) (*.f64 (+.f64 eps x) #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
98.0%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) eps))
50.0%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* eps -1/2)) x) (+ (* (* eps eps) -1/6) 1)) (*.f64 (-.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) eps) eps (/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)) x)) x)) #s(literal 1/2 binary64)) (*.f64 x x)))) eps))
98.2%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
98.0%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 eps x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
5.0%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) eps))
98.1%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
98.3%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
98.2%
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
98.1%
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps x) eps)))
100.0%
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))))
98.9%
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 #s(approx (* 2 (sin (* 1/2 eps))) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/24 binary64) eps)) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))))
Compiler

Compiled 797 to 617 computations (22.6% saved)

simplify98.0ms (0.8%)

Memory
10.2MiB live, 89.6MiB allocated
Algorithm
egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)
cost-diff0
#s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))
cost-diff0
(*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64))
cost-diff0
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
cost-diff0
#s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps))
cost-diff0
(fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x))
cost-diff0
(*.f64 (fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps)
cost-diff0
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
cost-diff0
(neg.f64 (*.f64 eps eps))
cost-diff0
(*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)))
cost-diff0
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))) (neg.f64 eps)))
cost-diff1280
(/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))) (neg.f64 eps))
cost-diff0
#s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))
cost-diff0
#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))))
cost-diff0
(*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) eps)
cost-diff0
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) eps))
cost-diff0
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
cost-diff0
(*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
cost-diff0
(*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))
cost-diff0
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))))
Rules
3 586×lower-fma.f32
3 576×lower-fma.f64
2 946×lower-*.f32
2 920×lower-*.f64
1 200×unsub-neg
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
075514
0105503
1185503
2432499
31054488
42164488
53134488
65144488
77405488
08040473
Stop Event
iter limit
node limit
iter limit
Calls
Call 1
Inputs
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))))
(*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))
(*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
#s(literal 2 binary64)
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 #s(literal 1/2 binary64) eps)
#s(literal 1/2 binary64)
eps
#s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(fma.f64 eps #s(literal 1/2 binary64) x)
x
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) eps))
(*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) eps)
#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))))
#s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))
(*.f64 (*.f64 x x) #s(literal -1/2 binary64))
(*.f64 x x)
x
#s(literal -1/2 binary64)
eps
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))) (neg.f64 eps)))
(/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))) (neg.f64 eps))
(*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)))
(neg.f64 (*.f64 eps eps))
(*.f64 eps eps)
eps
#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))
#s(literal 1 binary64)
(neg.f64 eps)
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
(*.f64 (fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps)
(fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x))
#s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps))
(*.f64 #s(literal -1/6 binary64) eps)
#s(literal -1/6 binary64)
eps
(cos.f64 x)
x
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64))
#s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)
(fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64))
#s(literal 1/3840 binary64)
(*.f64 eps eps)
eps
#s(literal -1/48 binary64)
#s(literal 1/2 binary64)
#s(literal 2 binary64)
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))
(fma.f64 #s(literal 2 binary64) x eps)
x
#s(literal -2 binary64)
Outputs
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))))
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 #s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) #s(literal 2 binary64)))
(*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))
(*.f64 (*.f64 #s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) #s(literal -2 binary64))
#s(literal 2 binary64)
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(*.f64 #s(literal 1/2 binary64) eps)
(*.f64 eps #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
eps
#s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(fma.f64 eps #s(literal 1/2 binary64) x)
x
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) eps))
(*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) eps)
#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))))
#s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))
(*.f64 (*.f64 x x) #s(literal -1/2 binary64))
(*.f64 x x)
x
#s(literal -1/2 binary64)
eps
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
(/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))) (neg.f64 eps))
(*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)
(*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)))
(*.f64 (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps) (neg.f64 eps))
(neg.f64 (*.f64 eps eps))
(*.f64 (neg.f64 eps) eps)
(*.f64 eps eps)
eps
#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))
#s(literal 1 binary64)
(neg.f64 eps)
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
(*.f64 (fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps)
(fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x))
#s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps))
(*.f64 #s(literal -1/6 binary64) eps)
#s(literal -1/6 binary64)
eps
(cos.f64 x)
x
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(*.f64 (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal -2 binary64))) (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)))
(*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64))
#s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)
(fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64))
#s(literal 1/3840 binary64)
(*.f64 eps eps)
eps
#s(literal -1/48 binary64)
#s(literal 1/2 binary64)
#s(literal 2 binary64)
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
(cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal -2 binary64)))
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))
(/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal -2 binary64))
(fma.f64 #s(literal 2 binary64) x eps)
(fma.f64 x #s(literal 2 binary64) eps)
x
#s(literal -2 binary64)

localize258.0ms (2.2%)

Memory
-0.9MiB live, 360.3MiB allocated
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
accuracy0.0078125
(fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64))
accuracy0.015625
(fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64))
accuracy0.03142341452874396
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
accuracy0.5291936054721119
#s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))
accuracy0.01171875
(*.f64 (fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps)
accuracy0.28515625
(*.f64 #s(literal -1/6 binary64) eps)
accuracy0.6894019019108873
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
accuracy59.15464355467415
#s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps))
accuracy0.0078125
(*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)))
accuracy0.7730052602805118
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))) (neg.f64 eps)))
accuracy1.2137897108165974
#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))
accuracy28.817999124056648
(/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))) (neg.f64 eps))
accuracy0.01171875
(*.f64 (*.f64 x x) #s(literal -1/2 binary64))
accuracy0.7730052602805118
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) eps))
accuracy1.1064928042398687
#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))))
accuracy61.9978301991907
#s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))
accuracy0
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))))
accuracy0
#s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
accuracy0.00390625
(*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))
accuracy0.03142341452874396
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
Samples
106.0ms177×0valid
104.0ms78×1valid
2.0ms3valid
Compiler

Compiled 329 to 65 computations (80.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 174.0ms
ival-add: 82.0ms (47% of total)
ival-mult: 44.0ms (25.2% of total)
adjust: 11.0ms (6.3% of total)
const: 10.0ms (5.7% of total)
ival-cos: 10.0ms (5.7% of total)
ival-sin: 8.0ms (4.6% of total)
ival-div: 4.0ms (2.3% of total)
ival-neg: 3.0ms (1.7% of total)
ival-sub: 2.0ms (1.1% of total)
exact: 1.0ms (0.6% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series69.0ms (0.6%)

Memory
-38.9MiB live, 40.9MiB allocated
Counts
28 → 552
Calls
Call 1
Inputs
#s(alt #s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))) (patch #s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))) #<representation binary64>) () ())
#s(alt (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) (patch (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) #<representation binary64>) () ())
#s(alt (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (patch (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #<representation binary64>) () ())
#s(alt (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (patch (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #<representation binary64>) () ())
#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) eps)) #<representation binary64>) () ())
#s(alt (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) eps) (patch (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) eps) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) (patch #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))) (patch #s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))) #<representation binary64>) () ())
#s(alt (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))) (neg.f64 eps)) (patch (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))) (neg.f64 eps)) #<representation binary64>) () ())
#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))) (neg.f64 eps))) (patch #s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))) (neg.f64 eps))) #<representation binary64>) () ())
#s(alt (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))) (patch (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (neg.f64 (*.f64 eps eps)) (patch (neg.f64 (*.f64 eps eps)) #<representation binary64>) () ())
#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps)) #<representation binary64>) () ())
#s(alt (*.f64 (fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps) (patch (*.f64 (fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps) #<representation binary64>) () ())
#s(alt (fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) (patch (fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) #<representation binary64>) () ())
#s(alt #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps)) (patch #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps)) #<representation binary64>) () ())
#s(alt (*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) (patch (*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) #<representation binary64>) () ())
#s(alt (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (patch (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) (patch #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #<representation binary64>) () ())
#s(alt (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps) (patch (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps) #<representation binary64>) () ())
#s(alt (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (patch (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #<representation binary64>) () ())
#s(alt #s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (patch #s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #<representation binary64>) () ())
#s(alt (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) (patch (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) (patch #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (*.f64 #s(literal -1/6 binary64) eps) (patch (*.f64 #s(literal -1/6 binary64) eps) #<representation binary64>) () ())
#s(alt (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (patch (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (patch (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) (patch (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())
Outputs
#s(alt (* eps (cos (* -1 x))) (taylor 0 eps) (#s(alt #s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))) (patch #s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))) (taylor 0 eps) (#s(alt #s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))) (patch #s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))) (taylor 0 eps) (#s(alt #s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))) (patch #s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))) (taylor 0 eps) (#s(alt #s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))) (patch #s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))) #<representation binary64>) () ())) ())
#s(alt (* eps (cos (neg x))) (taylor 0 eps) (#s(alt (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) (patch (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos (neg x)) (* 1/2 (* eps (sin (neg x)))))) (taylor 0 eps) (#s(alt (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) (patch (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos (neg x)) (* eps (+ (* 1/2 (sin (neg x))) (* 2 (* eps (+ (* -1/16 (cos (neg x))) (* -1/48 (cos (neg x)))))))))) (taylor 0 eps) (#s(alt (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) (patch (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos (neg x)) (* eps (+ (* 1/2 (sin (neg x))) (* eps (+ (* -1/24 (* eps (sin (neg x)))) (* 2 (+ (* -1/16 (cos (neg x))) (* -1/48 (cos (neg x))))))))))) (taylor 0 eps) (#s(alt (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) (patch (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 eps) (#s(alt (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (patch (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (* -1/24 (pow eps 2)))) (taylor 0 eps) (#s(alt (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (patch (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24)))) (taylor 0 eps) (#s(alt (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (patch (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24)))) (taylor 0 eps) (#s(alt (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (patch (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 eps) (taylor 0 eps) (#s(alt (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (patch (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1/2 (* -1/48 (pow eps 2)))) (taylor 0 eps) (#s(alt (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (patch (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))) (taylor 0 eps) (#s(alt (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (patch (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))) (taylor 0 eps) (#s(alt (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (patch (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (cos x)) (taylor 0 eps) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* -1/2 (* eps (sin x))))) (taylor 0 eps) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) (taylor 0 eps) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))) (taylor 0 eps) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (cos x)) (taylor 0 eps) (#s(alt (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) eps) (patch (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* -1/2 (* eps (sin x))))) (taylor 0 eps) (#s(alt (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) eps) (patch (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) eps) #<representation binary64>) () ())) ())
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Calls

6 calls:

TimeVariablePointExpression
26.0ms
eps
@0
((* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (* 2 (sin (* 1/2 eps))) (cos (+ (* eps -1/2) (neg x)))) (* 2 (sin (* 1/2 eps))) (sin (* 1/2 eps)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (+ (* (* (+ eps x) -1/2) x) 1) (/ (* (neg (* eps eps)) (+ (* (* (sin x) -1/2) eps) (cos x))) (neg eps)) (- (sin (+ x eps)) (sin x)) (* (neg (* eps eps)) (+ (* (* (sin x) -1/2) eps) (cos x))) (neg (* eps eps)) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (* 1/2 (+ 0 eps))) 2) (sin (* 1/2 (+ 0 eps))) (* (+ (* (+ (* 1/3840 (* eps eps)) -1/48) (* eps eps)) 1/2) eps) (cos (+ (* eps 1/2) x)) (cos (+ (* eps -1/2) (neg x))) (* (* x x) -1/2) (+ (* (* (sin x) -1/2) eps) (cos x)) (* -1/6 eps) (cos (/ (+ (* 2 x) eps) -2)) (+ (* 1/3840 (* eps eps)) -1/48) (+ (* (+ (* 1/3840 (* eps eps)) -1/48) (* eps eps)) 1/2))
4.0ms
eps
@inf
((* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (* 2 (sin (* 1/2 eps))) (cos (+ (* eps -1/2) (neg x)))) (* 2 (sin (* 1/2 eps))) (sin (* 1/2 eps)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (+ (* (* (+ eps x) -1/2) x) 1) (/ (* (neg (* eps eps)) (+ (* (* (sin x) -1/2) eps) (cos x))) (neg eps)) (- (sin (+ x eps)) (sin x)) (* (neg (* eps eps)) (+ (* (* (sin x) -1/2) eps) (cos x))) (neg (* eps eps)) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (* 1/2 (+ 0 eps))) 2) (sin (* 1/2 (+ 0 eps))) (* (+ (* (+ (* 1/3840 (* eps eps)) -1/48) (* eps eps)) 1/2) eps) (cos (+ (* eps 1/2) x)) (cos (+ (* eps -1/2) (neg x))) (* (* x x) -1/2) (+ (* (* (sin x) -1/2) eps) (cos x)) (* -1/6 eps) (cos (/ (+ (* 2 x) eps) -2)) (+ (* 1/3840 (* eps eps)) -1/48) (+ (* (+ (* 1/3840 (* eps eps)) -1/48) (* eps eps)) 1/2))
4.0ms
eps
@-inf
((* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (* 2 (sin (* 1/2 eps))) (cos (+ (* eps -1/2) (neg x)))) (* 2 (sin (* 1/2 eps))) (sin (* 1/2 eps)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (+ (* (* (+ eps x) -1/2) x) 1) (/ (* (neg (* eps eps)) (+ (* (* (sin x) -1/2) eps) (cos x))) (neg eps)) (- (sin (+ x eps)) (sin x)) (* (neg (* eps eps)) (+ (* (* (sin x) -1/2) eps) (cos x))) (neg (* eps eps)) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (* 1/2 (+ 0 eps))) 2) (sin (* 1/2 (+ 0 eps))) (* (+ (* (+ (* 1/3840 (* eps eps)) -1/48) (* eps eps)) 1/2) eps) (cos (+ (* eps 1/2) x)) (cos (+ (* eps -1/2) (neg x))) (* (* x x) -1/2) (+ (* (* (sin x) -1/2) eps) (cos x)) (* -1/6 eps) (cos (/ (+ (* 2 x) eps) -2)) (+ (* 1/3840 (* eps eps)) -1/48) (+ (* (+ (* 1/3840 (* eps eps)) -1/48) (* eps eps)) 1/2))
3.0ms
x
@inf
((* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (* 2 (sin (* 1/2 eps))) (cos (+ (* eps -1/2) (neg x)))) (* 2 (sin (* 1/2 eps))) (sin (* 1/2 eps)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (+ (* (* (+ eps x) -1/2) x) 1) (/ (* (neg (* eps eps)) (+ (* (* (sin x) -1/2) eps) (cos x))) (neg eps)) (- (sin (+ x eps)) (sin x)) (* (neg (* eps eps)) (+ (* (* (sin x) -1/2) eps) (cos x))) (neg (* eps eps)) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (* 1/2 (+ 0 eps))) 2) (sin (* 1/2 (+ 0 eps))) (* (+ (* (+ (* 1/3840 (* eps eps)) -1/48) (* eps eps)) 1/2) eps) (cos (+ (* eps 1/2) x)) (cos (+ (* eps -1/2) (neg x))) (* (* x x) -1/2) (+ (* (* (sin x) -1/2) eps) (cos x)) (* -1/6 eps) (cos (/ (+ (* 2 x) eps) -2)) (+ (* 1/3840 (* eps eps)) -1/48) (+ (* (+ (* 1/3840 (* eps eps)) -1/48) (* eps eps)) 1/2))
3.0ms
x
@-inf
((* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (* 2 (sin (* 1/2 eps))) (cos (+ (* eps -1/2) (neg x)))) (* 2 (sin (* 1/2 eps))) (sin (* 1/2 eps)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (+ (* (* (+ eps x) -1/2) x) 1) (/ (* (neg (* eps eps)) (+ (* (* (sin x) -1/2) eps) (cos x))) (neg eps)) (- (sin (+ x eps)) (sin x)) (* (neg (* eps eps)) (+ (* (* (sin x) -1/2) eps) (cos x))) (neg (* eps eps)) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (* 1/2 (+ 0 eps))) 2) (sin (* 1/2 (+ 0 eps))) (* (+ (* (+ (* 1/3840 (* eps eps)) -1/48) (* eps eps)) 1/2) eps) (cos (+ (* eps 1/2) x)) (cos (+ (* eps -1/2) (neg x))) (* (* x x) -1/2) (+ (* (* (sin x) -1/2) eps) (cos x)) (* -1/6 eps) (cos (/ (+ (* 2 x) eps) -2)) (+ (* 1/3840 (* eps eps)) -1/48) (+ (* (+ (* 1/3840 (* eps eps)) -1/48) (* eps eps)) 1/2))

simplify192.0ms (1.6%)

Memory
43.6MiB live, 233.2MiB allocated
Algorithm
egg-herbie
Rules
17 708×lower-fma.f64
17 708×lower-fma.f32
6 378×lower-*.f64
6 378×lower-*.f32
4 182×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04766142
115295822
238425766
084105318
Stop Event
iter limit
node limit
Counts
552 → 548
Calls
Call 1
Inputs
(* eps (cos (* -1 x)))
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))))
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))))
(* eps (cos (neg x)))
(* eps (+ (cos (neg x)) (* 1/2 (* eps (sin (neg x))))))
(* eps (+ (cos (neg x)) (* eps (+ (* 1/2 (sin (neg x))) (* 2 (* eps (+ (* -1/16 (cos (neg x))) (* -1/48 (cos (neg x))))))))))
(* eps (+ (cos (neg x)) (* eps (+ (* 1/2 (sin (neg x))) (* eps (+ (* -1/24 (* eps (sin (neg x)))) (* 2 (+ (* -1/16 (cos (neg x))) (* -1/48 (cos (neg x)))))))))))
eps
(* eps (+ 1 (* -1/24 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24))))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* -1 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1 (cos x)) (* 1/2 (* eps (sin x)))))
(* (pow eps 2) (+ (* -1 (cos x)) (* 1/2 (* eps (sin x)))))
(* (pow eps 2) (+ (* -1 (cos x)) (* 1/2 (* eps (sin x)))))
(* -1 (pow eps 2))
(* -1 (pow eps 2))
(* -1 (pow eps 2))
(* -1 (pow eps 2))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(* -1/2 (sin x))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(* eps (cos (* -1 x)))
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))))
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))))
eps
(* eps (+ 1 (* -1/24 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24))))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(cos (neg x))
(+ (cos (neg x)) (* 1/2 (* eps (sin (neg x)))))
(+ (cos (neg x)) (* eps (- (* -1/8 (* eps (cos (neg x)))) (* -1/2 (sin (neg x))))))
(+ (cos (neg x)) (* eps (- (* eps (+ (* -1/8 (cos (neg x))) (* -1/48 (* eps (sin (neg x)))))) (* -1/2 (sin (neg x))))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(cos (* -1 x))
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))
(+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x))))))
(+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x))))))
-1/48
(- (* 1/3840 (pow eps 2)) 1/48)
(- (* 1/3840 (pow eps 2)) 1/48)
(- (* 1/3840 (pow eps 2)) 1/48)
1/2
(+ 1/2 (* -1/48 (pow eps 2)))
(+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))
(+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (neg (+ x (* 1/2 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (neg (+ x (* 1/2 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (neg (+ x (* 1/2 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (neg (+ x (* 1/2 eps)))) (sin (* 1/2 eps))))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps (sin x)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps x))
(* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* 1/2 (* (pow eps 3) (sin x)))
(* (pow eps 3) (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))))
(* (pow eps 3) (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))))
(* (pow eps 3) (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))))
(* -1 (pow eps 2))
(* -1 (pow eps 2))
(* -1 (pow eps 2))
(* -1 (pow eps 2))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* -1/6 (* (pow eps 3) (cos x)))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* -1/6 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* -1/6 (* eps (cos x)))
(* eps (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* eps (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* eps (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(* 1/3840 (pow eps 5))
(* (pow eps 5) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(* (pow eps 5) (- (+ 1/3840 (/ 1/2 (pow eps 4))) (* 1/48 (/ 1 (pow eps 2)))))
(* (pow eps 5) (- (+ 1/3840 (/ 1/2 (pow eps 4))) (* 1/48 (/ 1 (pow eps 2)))))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (neg (+ x (* 1/2 eps))))
(cos (neg (+ x (* 1/2 eps))))
(cos (neg (+ x (* 1/2 eps))))
(cos (neg (+ x (* 1/2 eps))))
(* -1/2 (* eps (sin x)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(cos (* -1/2 (+ eps (* 2 x))))
(cos (* -1/2 (+ eps (* 2 x))))
(cos (* -1/2 (+ eps (* 2 x))))
(cos (* -1/2 (+ eps (* 2 x))))
(* 1/3840 (pow eps 2))
(* (pow eps 2) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(* 1/3840 (pow eps 4))
(* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(* (pow eps 4) (- (+ 1/3840 (/ 1/2 (pow eps 4))) (* 1/48 (/ 1 (pow eps 2)))))
(* (pow eps 4) (- (+ 1/3840 (/ 1/2 (pow eps 4))) (* 1/48 (/ 1 (pow eps 2)))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (- (* -1/2 eps) x)) (sin (* 1/2 eps))))
(* 2 (* (cos (- (* -1/2 eps) x)) (sin (* 1/2 eps))))
(* 2 (* (cos (- (* -1/2 eps) x)) (sin (* 1/2 eps))))
(* 2 (* (cos (- (* -1/2 eps) x)) (sin (* 1/2 eps))))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps (sin x)))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1/2 (* eps x))
(* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x))))
(* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x))))
(* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x))))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(* 1/2 (* (pow eps 3) (sin x)))
(* -1 (* (pow eps 3) (+ (* -1/2 (sin x)) (/ (cos x) eps))))
(* -1 (* (pow eps 3) (+ (* -1/2 (sin x)) (/ (cos x) eps))))
(* -1 (* (pow eps 3) (+ (* -1/2 (sin x)) (/ (cos x) eps))))
(* -1 (pow eps 2))
(* -1 (pow eps 2))
(* -1 (pow eps 2))
(* -1 (pow eps 2))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(* -1/6 (* (pow eps 3) (cos x)))
(* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))
(* -1/6 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))
(* -1/6 (* eps (cos x)))
(* -1 (* eps (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))
(* -1 (* eps (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))
(* -1 (* eps (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(* 1/3840 (pow eps 5))
(* -1 (* (pow eps 5) (- (* 1/48 (/ 1 (pow eps 2))) 1/3840)))
(* -1 (* (pow eps 5) (- (* 1/48 (/ 1 (pow eps 2))) (+ 1/3840 (/ 1/2 (pow eps 4))))))
(* -1 (* (pow eps 5) (- (* 1/48 (/ 1 (pow eps 2))) (+ 1/3840 (/ 1/2 (pow eps 4))))))
(cos (- x (* -1/2 eps)))
(cos (- x (* -1/2 eps)))
(cos (- x (* -1/2 eps)))
(cos (- x (* -1/2 eps)))
(cos (- (* -1/2 eps) x))
(cos (- (* -1/2 eps) x))
(cos (- (* -1/2 eps) x))
(cos (- (* -1/2 eps) x))
(* -1/2 (* eps (sin x)))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(cos (* -1/2 (- (* 2 x) (* -1 eps))))
(cos (* -1/2 (- (* 2 x) (* -1 eps))))
(cos (* -1/2 (- (* 2 x) (* -1 eps))))
(cos (* -1/2 (- (* 2 x) (* -1 eps))))
(* 1/3840 (pow eps 2))
(* (pow eps 2) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(* 1/3840 (pow eps 4))
(* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(* (pow eps 4) (- (+ 1/3840 (/ 1/2 (pow eps 4))) (* 1/48 (/ 1 (pow eps 2)))))
(* (pow eps 4) (- (+ 1/3840 (/ 1/2 (pow eps 4))) (* 1/48 (/ 1 (pow eps 2)))))
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* x (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* -1/3 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))))))))
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* x (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* -1/3 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))))))))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
1
(+ 1 (* -1/2 (* eps x)))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
1
(+ 1 (* -1/2 (* eps x)))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(* -1 (pow eps 2))
(+ (* -1 (pow eps 2)) (* 1/2 (* (pow eps 3) x)))
(+ (* -1 (pow eps 2)) (* x (+ (* 1/2 (* (pow eps 2) x)) (* 1/2 (pow eps 3)))))
(+ (* -1 (pow eps 2)) (* x (+ (* 1/2 (pow eps 3)) (* x (+ (* -1/12 (* (pow eps 3) x)) (* 1/2 (pow eps 2)))))))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* 1/12 (* (pow eps 2) x)) (* eps (- (* 1/12 (pow eps 2)) 1/2)))))))
(+ 1 (* -1/6 (pow eps 2)))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2))))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2))))))
(* -1/6 eps)
(+ (* -1/2 x) (* -1/6 eps))
(+ (* -1/6 eps) (* x (- (* 1/12 (* eps x)) 1/2)))
(+ (* -1/6 eps) (* x (- (* x (+ (* 1/12 eps) (* 1/12 x))) 1/2)))
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* x (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* -1/3 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))))))))
(cos (* 1/2 eps))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))
(cos (* -1/2 eps))
(+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps))))
(+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (* -1 (sin (* -1/2 eps))))))
(+ (cos (* -1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* -1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps)))))) (* -1 (sin (* -1/2 eps))))))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
1
(+ 1 (* -1/2 (* eps x)))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(cos (* -1/2 eps))
(+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps))))
(+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (* -1 (sin (* -1/2 eps))))))
(+ (cos (* -1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* -1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps)))))) (* -1 (sin (* -1/2 eps))))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (- (* -1/2 eps) x)) (sin (* 1/2 eps))))
(* 2 (* (cos (- (* -1/2 eps) x)) (sin (* 1/2 eps))))
(* 2 (* (cos (- (* -1/2 eps) x)) (sin (* 1/2 eps))))
(* 2 (* (cos (- (* -1/2 eps) x)) (sin (* 1/2 eps))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* -1/2 (pow x 2))
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (/ 1 (pow x 2))) 1/2))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (/ 1 (pow x 2))) 1/2))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* -1 (* (pow eps 2) (+ (cos x) (* -1/2 (* eps (sin x))))))
(* -1 (* (pow eps 2) (+ (cos x) (* -1/2 (* eps (sin x))))))
(* -1 (* (pow eps 2) (+ (cos x) (* -1/2 (* eps (sin x))))))
(* -1 (* (pow eps 2) (+ (cos x) (* -1/2 (* eps (sin x))))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (- (* -1/2 eps) x))
(cos (- (* -1/2 eps) x))
(cos (- (* -1/2 eps) x))
(cos (- (* -1/2 eps) x))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(cos (* -1/2 (+ eps (* 2 x))))
(cos (* -1/2 (+ eps (* 2 x))))
(cos (* -1/2 (+ eps (* 2 x))))
(cos (* -1/2 (+ eps (* 2 x))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (+ (* -1 x) (* -1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (+ (* -1 x) (* -1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (+ (* -1 x) (* -1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (+ (* -1 x) (* -1/2 eps))) (sin (* 1/2 eps))))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* -1/2 (pow x 2))
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))
(* (pow x 2) (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2))
(* (pow x 2) (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* -1 (* (pow eps 2) (+ (cos x) (* -1/2 (* eps (sin x))))))
(* -1 (* (pow eps 2) (+ (cos x) (* -1/2 (* eps (sin x))))))
(* -1 (* (pow eps 2) (+ (cos x) (* -1/2 (* eps (sin x))))))
(* -1 (* (pow eps 2) (+ (cos x) (* -1/2 (* eps (sin x))))))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(cos (- (* 1/2 eps) (* -1 x)))
(cos (- (* 1/2 eps) (* -1 x)))
(cos (- (* 1/2 eps) (* -1 x)))
(cos (- (* 1/2 eps) (* -1 x)))
(cos (+ (* -1 x) (* -1/2 eps)))
(cos (+ (* -1 x) (* -1/2 eps)))
(cos (+ (* -1 x) (* -1/2 eps)))
(cos (+ (* -1 x) (* -1/2 eps)))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(cos (* -1/2 (- eps (* -2 x))))
(cos (* -1/2 (- eps (* -2 x))))
(cos (* -1/2 (- eps (* -2 x))))
(cos (* -1/2 (- eps (* -2 x))))
Outputs
(* eps (cos (* -1 x)))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))))
(*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
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eps
(+ eps (* -1/2 (* (pow eps 2) x)))
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(sin eps)
(sin.f64 eps)
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(* -1/2 (pow x 2))
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(* -1/2 (pow x 2))
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(* -1/2 (pow x 2))
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(*.f64 (*.f64 x x) #s(literal -1/2 binary64))
1
#s(literal 1 binary64)
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(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(fma.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x))
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(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(fma.f64 (*.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps (*.f64 (sin.f64 x) #s(literal -1/2 binary64)))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(fma.f64 (*.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps (*.f64 (sin.f64 x) #s(literal -1/2 binary64)))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(fma.f64 (*.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps (*.f64 (sin.f64 x) #s(literal -1/2 binary64)))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(fma.f64 (*.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps (*.f64 (sin.f64 x) #s(literal -1/2 binary64)))
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(cos (+ x (* 1/2 eps)))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (- (* -1/2 eps) x))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (- (* -1/2 eps) x))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (- (* -1/2 eps) x))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (- (* -1/2 eps) x))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(* -1/2 (pow x 2))
(*.f64 (*.f64 x x) #s(literal -1/2 binary64))
(* -1/2 (pow x 2))
(*.f64 (*.f64 x x) #s(literal -1/2 binary64))
(* -1/2 (pow x 2))
(*.f64 (*.f64 x x) #s(literal -1/2 binary64))
(* -1/2 (pow x 2))
(*.f64 (*.f64 x x) #s(literal -1/2 binary64))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x))
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(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x))
(cos (* -1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* -1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* -1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* -1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
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(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
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(* 2 (* (cos (+ (* -1 x) (* -1/2 eps))) (sin (* 1/2 eps))))
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
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(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
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(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
(* 2 (* (cos (+ (* -1 x) (* -1/2 eps))) (sin (* 1/2 eps))))
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x))
(* -1/2 (pow x 2))
(*.f64 (*.f64 x x) #s(literal -1/2 binary64))
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))
(*.f64 (*.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) x) x)
(* (pow x 2) (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2))
(*.f64 (-.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/2 binary64)) (*.f64 x x))
(* (pow x 2) (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2))
(*.f64 (-.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/2 binary64)) (*.f64 x x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(* -1 (* (pow eps 2) (+ (cos x) (* -1/2 (* eps (sin x))))))
(*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) (*.f64 (neg.f64 eps) eps))
(* -1 (* (pow eps 2) (+ (cos x) (* -1/2 (* eps (sin x))))))
(*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) (*.f64 (neg.f64 eps) eps))
(* -1 (* (pow eps 2) (+ (cos x) (* -1/2 (* eps (sin x))))))
(*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) (*.f64 (neg.f64 eps) eps))
(* -1 (* (pow eps 2) (+ (cos x) (* -1/2 (* eps (sin x))))))
(*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) (*.f64 (neg.f64 eps) eps))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(fma.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(fma.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(fma.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(fma.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(fma.f64 (*.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps (*.f64 (sin.f64 x) #s(literal -1/2 binary64)))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(fma.f64 (*.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps (*.f64 (sin.f64 x) #s(literal -1/2 binary64)))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(fma.f64 (*.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps (*.f64 (sin.f64 x) #s(literal -1/2 binary64)))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(fma.f64 (*.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps (*.f64 (sin.f64 x) #s(literal -1/2 binary64)))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
(cos (- (* 1/2 eps) (* -1 x)))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (- (* 1/2 eps) (* -1 x)))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (- (* 1/2 eps) (* -1 x)))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (- (* 1/2 eps) (* -1 x)))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (+ (* -1 x) (* -1/2 eps)))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (+ (* -1 x) (* -1/2 eps)))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (+ (* -1 x) (* -1/2 eps)))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (+ (* -1 x) (* -1/2 eps)))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(* -1/2 (pow x 2))
(*.f64 (*.f64 x x) #s(literal -1/2 binary64))
(* -1/2 (pow x 2))
(*.f64 (*.f64 x x) #s(literal -1/2 binary64))
(* -1/2 (pow x 2))
(*.f64 (*.f64 x x) #s(literal -1/2 binary64))
(* -1/2 (pow x 2))
(*.f64 (*.f64 x x) #s(literal -1/2 binary64))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x))
(cos (* -1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* -1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* -1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* -1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))

rewrite208.0ms (1.7%)

Memory
-42.2MiB live, 288.6MiB allocated
Rules
4 508×lower-*.f32
4 482×lower-*.f64
4 368×lower-fma.f32
4 358×lower-fma.f64
3 704×lower-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
075465
0105454
1372442
22863442
08496427
Stop Event
iter limit
node limit
iter limit
Counts
28 → 351
Calls
Call 1
Inputs
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))))
(*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))
(*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) eps))
(*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) eps)
#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))))
#s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))
(/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))) (neg.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))) (neg.f64 eps)))
(*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)))
(neg.f64 (*.f64 eps eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
(*.f64 (fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps)
(fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x))
#s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps))
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64))
#s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
#s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(*.f64 (*.f64 x x) #s(literal -1/2 binary64))
#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))
(*.f64 #s(literal -1/6 binary64) eps)
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
(fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64))
(fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64))
Outputs
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 #s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) #s(literal 2 binary64)))
(*.f64 (*.f64 #s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal 2 binary64)) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))
(*.f64 (*.f64 #s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(*.f64 #s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(*.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) #s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) #s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))))
(*.f64 #s(literal 2 binary64) (*.f64 #s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))
(fma.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 1 binary64) (*.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 0 binary64)))
(fma.f64 #s(literal 0 binary64) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 1 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(+.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 1 binary64)) (*.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 0 binary64)))
(+.f64 (*.f64 #s(literal 0 binary64) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 #s(literal 1 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) eps))
(*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) eps)
(*.f64 eps #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))))
(/.f64 (neg.f64 (*.f64 (pow.f64 eps #s(literal 3 binary64)) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))))) (*.f64 (neg.f64 eps) eps))
(/.f64 (neg.f64 (*.f64 (*.f64 (neg.f64 eps) eps) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))))) eps)
(/.f64 (neg.f64 (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) (pow.f64 eps #s(literal 3 binary64)))) (*.f64 (neg.f64 eps) eps))
(/.f64 (neg.f64 (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) (*.f64 (neg.f64 eps) eps))) eps)
(/.f64 (*.f64 (pow.f64 eps #s(literal 3 binary64)) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))))) (*.f64 eps eps))
(/.f64 (*.f64 (*.f64 (neg.f64 eps) eps) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))))) (neg.f64 eps))
(/.f64 (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) (pow.f64 eps #s(literal 3 binary64))) (*.f64 eps eps))
(/.f64 (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) (*.f64 (neg.f64 eps) eps)) (neg.f64 eps))
(fma.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) eps (*.f64 #s(literal 0 binary64) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))))))
(fma.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) eps (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) #s(literal 0 binary64)))
(fma.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) #s(literal 0 binary64) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) eps))
(fma.f64 eps #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) (*.f64 #s(literal 0 binary64) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))))))
(fma.f64 eps #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) #s(literal 0 binary64)))
(fma.f64 #s(literal 0 binary64) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) eps))
(+.f64 (*.f64 #s(literal 0 binary64) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))))) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) eps))
(+.f64 (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) #s(literal 0 binary64)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) eps))
(+.f64 (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) eps) (*.f64 #s(literal 0 binary64) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))))))
(+.f64 (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) eps) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) #s(literal 0 binary64)))
#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))))
#s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal -1 binary64) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))) #s(literal -1 binary64)) (pow.f64 (/.f64 eps (*.f64 (neg.f64 eps) eps)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (pow.f64 eps #s(literal -2 binary64)) #s(literal -1 binary64)) (pow.f64 (/.f64 eps #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) #s(literal -1 binary64)) (neg.f64 eps))
(*.f64 (/.f64 (*.f64 (neg.f64 eps) eps) #s(literal -1 binary64)) (/.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
(*.f64 (/.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) (neg.f64 eps)) (*.f64 (neg.f64 eps) eps))
(*.f64 #s(literal -1 binary64) (*.f64 (*.f64 eps eps) (/.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) (neg.f64 eps))))
(*.f64 #s(literal -1 binary64) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) (neg.f64 eps)))
(*.f64 (/.f64 #s(literal -1 binary64) eps) (pow.f64 (/.f64 #s(literal -1 binary64) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) (*.f64 eps eps))) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal -1 binary64) eps) (*.f64 (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps) (neg.f64 eps)))
(*.f64 (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) (*.f64 eps eps)) (pow.f64 eps #s(literal -1 binary64)))
(*.f64 (neg.f64 eps) (*.f64 eps (/.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) (neg.f64 eps))))
(*.f64 (*.f64 (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps) (neg.f64 eps)) (/.f64 #s(literal -1 binary64) eps))
(*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)
(*.f64 (*.f64 (neg.f64 eps) eps) (/.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) (neg.f64 eps)))
(*.f64 #s(literal 1 binary64) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
(*.f64 eps (*.f64 (neg.f64 eps) (/.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) (neg.f64 eps))))
(pow.f64 (/.f64 (pow.f64 (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps) #s(literal -1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (pow.f64 (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps) #s(literal -1 binary64)) #s(literal -1 binary64))
(/.f64 (neg.f64 (/.f64 (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) (*.f64 eps eps)) #s(literal 1 binary64))) (neg.f64 eps))
(/.f64 (neg.f64 (*.f64 (*.f64 (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps) (neg.f64 eps)) #s(literal 1 binary64))) eps)
(/.f64 (/.f64 (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) (*.f64 eps eps)) #s(literal 1 binary64)) eps)
(/.f64 (*.f64 (*.f64 (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps) (neg.f64 eps)) #s(literal 1 binary64)) (neg.f64 eps))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (pow.f64 (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps) #s(literal -1 binary64)) #s(literal 1 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps) #s(literal -1 binary64))))
(/.f64 (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) (*.f64 eps eps)) eps)
(/.f64 (*.f64 (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps) (neg.f64 eps)) (neg.f64 eps))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (pow.f64 (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps) #s(literal -1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps) #s(literal -1 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps) #s(literal -1 binary64)))
(neg.f64 (*.f64 (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) (*.f64 eps eps)) (/.f64 #s(literal -1 binary64) eps)))
(neg.f64 (*.f64 (*.f64 eps eps) (/.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) (neg.f64 eps))))
(neg.f64 (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) (neg.f64 eps)))
(-.f64 #s(literal 0 binary64) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) (neg.f64 eps)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps) #s(literal -1 binary64))) #s(literal -1 binary64)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
(*.f64 (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) #s(literal -1 binary64)) (*.f64 eps eps))
(*.f64 (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) (neg.f64 eps)) eps)
(*.f64 #s(literal -1 binary64) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) (*.f64 eps eps)))
(*.f64 (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps) (neg.f64 eps))
(*.f64 (neg.f64 eps) (*.f64 eps #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))))
(*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) (*.f64 (neg.f64 eps) eps))
(*.f64 (*.f64 (neg.f64 eps) eps) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)))
(*.f64 (*.f64 eps eps) (neg.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))))
(*.f64 eps (*.f64 (neg.f64 eps) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))))
(neg.f64 (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) (*.f64 eps eps)))
(-.f64 #s(literal 0 binary64) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) (*.f64 eps eps)))
(*.f64 #s(literal -1 binary64) (*.f64 eps eps))
(*.f64 (neg.f64 eps) eps)
(*.f64 (*.f64 eps eps) #s(literal -1 binary64))
(*.f64 eps (neg.f64 eps))
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(/.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 (pow.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) #s(literal 2 binary64)) (pow.f64 eps #s(literal 4 binary64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) eps) eps)))
(/.f64 (neg.f64 (fma.f64 (pow.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) #s(literal 2 binary64)) (pow.f64 eps #s(literal 4 binary64)) #s(literal -1/4 binary64))) (neg.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal -1/2 binary64))))
(/.f64 (neg.f64 (fma.f64 (pow.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) #s(literal 3 binary64)) (pow.f64 eps #s(literal 6 binary64)) #s(literal 1/8 binary64))) (neg.f64 (+.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 (pow.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) #s(literal 2 binary64)) (pow.f64 eps #s(literal 4 binary64))) (*.f64 (*.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) eps) (*.f64 eps #s(literal 1/2 binary64)))))))
(/.f64 (neg.f64 (fma.f64 (pow.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) #s(literal 3 binary64)) (pow.f64 eps #s(literal 6 binary64)) #s(literal 1/8 binary64))) (neg.f64 (-.f64 (fma.f64 (pow.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) #s(literal 2 binary64)) (pow.f64 eps #s(literal 4 binary64)) #s(literal 1/4 binary64)) (*.f64 (*.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) eps) (*.f64 eps #s(literal 1/2 binary64))))))
(/.f64 (fma.f64 (pow.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) #s(literal 2 binary64)) (pow.f64 eps #s(literal 4 binary64)) #s(literal -1/4 binary64)) (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal -1/2 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal -1/2 binary64)) (fma.f64 (pow.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) #s(literal 2 binary64)) (pow.f64 eps #s(literal 4 binary64)) #s(literal -1/4 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 (fma.f64 (pow.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) #s(literal 2 binary64)) (pow.f64 eps #s(literal 4 binary64)) #s(literal 1/4 binary64)) (*.f64 (*.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) eps) (*.f64 eps #s(literal 1/2 binary64)))) (fma.f64 (pow.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) #s(literal 3 binary64)) (pow.f64 eps #s(literal 6 binary64)) #s(literal 1/8 binary64)))))
(/.f64 (fma.f64 (pow.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) #s(literal 3 binary64)) (pow.f64 eps #s(literal 6 binary64)) #s(literal 1/8 binary64)) (+.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 (pow.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) #s(literal 2 binary64)) (pow.f64 eps #s(literal 4 binary64))) (*.f64 (*.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) eps) (*.f64 eps #s(literal 1/2 binary64))))))
(/.f64 (fma.f64 (pow.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) #s(literal 3 binary64)) (pow.f64 eps #s(literal 6 binary64)) #s(literal 1/8 binary64)) (-.f64 (fma.f64 (pow.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) #s(literal 2 binary64)) (pow.f64 eps #s(literal 4 binary64)) #s(literal 1/4 binary64)) (*.f64 (*.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) eps) (*.f64 eps #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal -1/2 binary64)) (fma.f64 (pow.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) #s(literal 2 binary64)) (pow.f64 eps #s(literal 4 binary64)) #s(literal -1/4 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (fma.f64 (pow.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) #s(literal 2 binary64)) (pow.f64 eps #s(literal 4 binary64)) #s(literal 1/4 binary64)) (*.f64 (*.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) eps) (*.f64 eps #s(literal 1/2 binary64)))) (fma.f64 (pow.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) #s(literal 3 binary64)) (pow.f64 eps #s(literal 6 binary64)) #s(literal 1/8 binary64))))
(fma.f64 (*.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) eps) eps #s(literal 1/2 binary64))
(fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64))
(fma.f64 (*.f64 eps eps) (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))
(fma.f64 eps (*.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) eps) #s(literal 1/2 binary64))
(-.f64 (/.f64 (*.f64 (pow.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) #s(literal 2 binary64)) (pow.f64 eps #s(literal 4 binary64))) (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal -1/2 binary64))))
(+.f64 (*.f64 (*.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) eps) eps) #s(literal 1/2 binary64))
(+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) eps) eps))

eval131.0ms (1.1%)

Memory
26.5MiB live, 172.4MiB allocated
Compiler

Compiled 17 760 to 2 231 computations (87.4% saved)

prune35.0ms (0.3%)

Memory
20.1MiB live, 97.9MiB allocated
Pruning

27 alts after pruning (17 fresh and 10 done)

PrunedKeptTotal
New8936899
Fresh51116
Picked235
Done178
Total90127928
Accuracy
100.0%
Counts
928 → 27
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.8%
(fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (cos.f64 eps) (sin.f64 x) (neg.f64 (sin.f64 x))))
64.4%
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
34.8%
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (/.f64 #s(literal 1 binary64) (neg.f64 (*.f64 eps eps)))))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
99.1%
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (fma.f64 (*.f64 (*.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) eps) eps) eps (*.f64 eps #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
99.1%
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
53.3%
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64))))) (neg.f64 eps)))
53.1%
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(approx (* (neg (* eps eps)) (+ (* (* (sin x) -1/2) eps) (cos x))) (*.f64 (neg.f64 eps) eps)) (neg.f64 eps)))
98.9%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps))
98.5%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) eps))
98.5%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
98.5%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
98.3%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) x (*.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
98.1%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))) eps))
98.3%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 #s(approx (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* eps -1/2)) (*.f64 (+.f64 eps x) #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
98.0%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) eps))
50.0%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* eps -1/2)) x) (+ (* (* eps eps) -1/6) 1)) (*.f64 (-.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) eps) eps (/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)) x)) x)) #s(literal 1/2 binary64)) (*.f64 x x)))) eps))
98.2%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
98.0%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 eps x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
5.0%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) eps))
98.1%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
98.3%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
98.2%
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
98.1%
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps x) eps)))
100.0%
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))))
99.2%
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 #s(literal 2 binary64) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64)) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))))
98.9%
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 #s(literal 2 binary64) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps))) #s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))))
98.8%
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 #s(literal 2 binary64) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps))) #s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))))
Compiler

Compiled 1 046 to 545 computations (47.9% saved)

regimes57.0ms (0.5%)

Memory
-11.3MiB live, 37.3MiB allocated
Counts
40 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 eps x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(approx (* (neg (* eps eps)) (+ (* (* (sin x) -1/2) eps) (cos x))) (*.f64 (neg.f64 eps) eps)) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 #s(approx (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* eps -1/2)) (*.f64 (+.f64 eps x) #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 eps x) #s(literal -1/2 binary64)) x (*.f64 eps #s(literal -1/2 binary64))) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) x (*.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64))))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* eps -1/2)) x) (+ (* (* eps eps) -1/6) 1)) (*.f64 (-.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) eps) eps (/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)) x)) x)) #s(literal 1/2 binary64)) (*.f64 x x)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 #s(literal 2 binary64) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps))) #s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) eps))
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 #s(literal 2 binary64) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps))) #s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))))
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 (fma.f64 #s(approx (* 1/12 (+ eps x)) (*.f64 #s(literal 1/12 binary64) x)) x #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) x #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 #s(literal 2 binary64) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64)) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))))
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (fma.f64 (*.f64 (*.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) eps) eps) eps (*.f64 eps #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64)) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps))
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 #s(approx (* 2 (sin (* 1/2 eps))) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/24 binary64) eps)) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))))
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))))
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))))
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps))
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (/.f64 #s(literal 1 binary64) (neg.f64 (*.f64 eps eps)))))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (cos.f64 eps) (sin.f64 x) (neg.f64 (sin.f64 x))))
Outputs
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))))
Calls

3 calls:

35.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
10.0ms
x
10.0ms
eps
Results
AccuracySegmentsBranch
100.0%1x
100.0%1eps
100.0%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes30.0ms (0.2%)

Memory
6.7MiB live, 45.9MiB allocated
Counts
34 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 eps x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(approx (* (neg (* eps eps)) (+ (* (* (sin x) -1/2) eps) (cos x))) (*.f64 (neg.f64 eps) eps)) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 #s(approx (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* eps -1/2)) (*.f64 (+.f64 eps x) #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 eps x) #s(literal -1/2 binary64)) x (*.f64 eps #s(literal -1/2 binary64))) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) x (*.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64))))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* eps -1/2)) x) (+ (* (* eps eps) -1/6) 1)) (*.f64 (-.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) eps) eps (/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)) x)) x)) #s(literal 1/2 binary64)) (*.f64 x x)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 #s(literal 2 binary64) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps))) #s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) eps))
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 #s(literal 2 binary64) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps))) #s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))))
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 (fma.f64 #s(approx (* 1/12 (+ eps x)) (*.f64 #s(literal 1/12 binary64) x)) x #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) x #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 #s(literal 2 binary64) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64)) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))))
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (fma.f64 (*.f64 (*.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) eps) eps) eps (*.f64 eps #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64)) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps))
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 #s(approx (* 2 (sin (* 1/2 eps))) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/24 binary64) eps)) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))))
Outputs
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 #s(literal 2 binary64) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64)) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))))
Calls

3 calls:

10.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
9.0ms
eps
9.0ms
x
Results
AccuracySegmentsBranch
99.2%1x
99.2%1eps
99.2%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes27.0ms (0.2%)

Memory
-25.8MiB live, 49.4MiB allocated
Counts
27 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 eps x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(approx (* (neg (* eps eps)) (+ (* (* (sin x) -1/2) eps) (cos x))) (*.f64 (neg.f64 eps) eps)) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 #s(approx (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* eps -1/2)) (*.f64 (+.f64 eps x) #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 eps x) #s(literal -1/2 binary64)) x (*.f64 eps #s(literal -1/2 binary64))) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) x (*.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64))))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* eps -1/2)) x) (+ (* (* eps eps) -1/6) 1)) (*.f64 (-.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) eps) eps (/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)) x)) x)) #s(literal 1/2 binary64)) (*.f64 x x)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 #s(literal 2 binary64) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps))) #s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) eps))
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 #s(literal 2 binary64) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps))) #s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))))
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 (fma.f64 #s(approx (* 1/12 (+ eps x)) (*.f64 #s(literal 1/12 binary64) x)) x #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) x #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
Outputs
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
Calls

3 calls:

10.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
9.0ms
x
7.0ms
eps
Results
AccuracySegmentsBranch
99.1%1x
99.1%1eps
99.1%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes52.0ms (0.4%)

Memory
-5.1MiB live, 37.8MiB allocated
Counts
26 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 eps x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(approx (* (neg (* eps eps)) (+ (* (* (sin x) -1/2) eps) (cos x))) (*.f64 (neg.f64 eps) eps)) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 #s(approx (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* eps -1/2)) (*.f64 (+.f64 eps x) #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 eps x) #s(literal -1/2 binary64)) x (*.f64 eps #s(literal -1/2 binary64))) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) x (*.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64))))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* eps -1/2)) x) (+ (* (* eps eps) -1/6) 1)) (*.f64 (-.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) eps) eps (/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)) x)) x)) #s(literal 1/2 binary64)) (*.f64 x x)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 #s(literal 2 binary64) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps))) #s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) eps))
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 #s(literal 2 binary64) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps))) #s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))))
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 (fma.f64 #s(approx (* 1/12 (+ eps x)) (*.f64 #s(literal 1/12 binary64) x)) x #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) x #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
Outputs
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 #s(literal 2 binary64) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps))) #s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))))
Calls

3 calls:

37.0ms
x
7.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
7.0ms
eps
Results
AccuracySegmentsBranch
98.9%1x
98.9%1eps
98.9%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes19.0ms (0.2%)

Memory
20.5MiB live, 20.5MiB allocated
Counts
21 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 eps x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(approx (* (neg (* eps eps)) (+ (* (* (sin x) -1/2) eps) (cos x))) (*.f64 (neg.f64 eps) eps)) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 #s(approx (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* eps -1/2)) (*.f64 (+.f64 eps x) #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 eps x) #s(literal -1/2 binary64)) x (*.f64 eps #s(literal -1/2 binary64))) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) x (*.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64))))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* eps -1/2)) x) (+ (* (* eps eps) -1/6) 1)) (*.f64 (-.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) eps) eps (/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)) x)) x)) #s(literal 1/2 binary64)) (*.f64 x x)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 #s(literal 2 binary64) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps))) #s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) eps))
Outputs
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 #s(literal 2 binary64) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps))) #s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))))
Calls

3 calls:

6.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
6.0ms
x
6.0ms
eps
Results
AccuracySegmentsBranch
98.8%1x
98.8%1eps
98.8%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes32.0ms (0.3%)

Memory
-15.3MiB live, 23.0MiB allocated
Counts
19 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 eps x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(approx (* (neg (* eps eps)) (+ (* (* (sin x) -1/2) eps) (cos x))) (*.f64 (neg.f64 eps) eps)) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 #s(approx (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* eps -1/2)) (*.f64 (+.f64 eps x) #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 eps x) #s(literal -1/2 binary64)) x (*.f64 eps #s(literal -1/2 binary64))) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) x (*.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64))))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* eps -1/2)) x) (+ (* (* eps eps) -1/6) 1)) (*.f64 (-.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) eps) eps (/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)) x)) x)) #s(literal 1/2 binary64)) (*.f64 x x)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
Calls

3 calls:

20.0ms
x
5.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
5.0ms
eps
Results
AccuracySegmentsBranch
98.5%1x
98.5%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
98.5%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes16.0ms (0.1%)

Memory
21.0MiB live, 21.0MiB allocated
Counts
17 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 eps x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(approx (* (neg (* eps eps)) (+ (* (* (sin x) -1/2) eps) (cos x))) (*.f64 (neg.f64 eps) eps)) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 #s(approx (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* eps -1/2)) (*.f64 (+.f64 eps x) #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 eps x) #s(literal -1/2 binary64)) x (*.f64 eps #s(literal -1/2 binary64))) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) x (*.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64))))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* eps -1/2)) x) (+ (* (* eps eps) -1/6) 1)) (*.f64 (-.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) eps) eps (/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)) x)) x)) #s(literal 1/2 binary64)) (*.f64 x x)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
Calls

3 calls:

5.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
5.0ms
x
5.0ms
eps
Results
AccuracySegmentsBranch
98.3%1x
98.3%1eps
98.3%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes13.0ms (0.1%)

Memory
-17.2MiB live, 21.0MiB allocated
Counts
10 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 eps x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(approx (* (neg (* eps eps)) (+ (* (* (sin x) -1/2) eps) (cos x))) (*.f64 (neg.f64 eps) eps)) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))) (neg.f64 eps)))
Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
Calls

3 calls:

5.0ms
x
3.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
3.0ms
eps
Results
AccuracySegmentsBranch
98.2%1x
98.2%1eps
98.2%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes8.0ms (0.1%)

Memory
13.8MiB live, 13.8MiB allocated
Accuracy

Total -59.6b remaining (-4944%)

Threshold costs -59.6b (-4944%)

Counts
6 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (* (+ eps x) -1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 eps x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
Calls

3 calls:

3.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
2.0ms
x
2.0ms
eps
Results
AccuracySegmentsBranch
98.1%1x
98.1%1eps
98.1%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Compiler

Compiled 9 to 10 computations (-11.1% saved)

simplify30.0ms (0.2%)

Memory
0.3MiB live, 39.2MiB allocated
Algorithm
egg-herbie
Rules
38×*-commutative-binary64-*.f64
1-exp-binary32-exp.f32
1-exp-binary64-exp.f64
+-commutative-binary64-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
089306
1111306
Stop Event
saturated
Calls
Call 1
Inputs
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))))
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 #s(literal 2 binary64) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64)) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))))
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 #s(literal 2 binary64) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps))) #s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))))
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 #s(literal 2 binary64) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps))) #s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
Outputs
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))))
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 #s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))))
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 #s(literal 2 binary64) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64)) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))))
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64)) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) #s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))))
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(*.f64 #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)))
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 #s(literal 2 binary64) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps))) #s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))))
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) #s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))))
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 #s(literal 2 binary64) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps))) #s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))))
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 #s(approx (sin (* 1/2 eps)) (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) #s(approx (cos (+ (* eps -1/2) (neg x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))

soundness1.3s (10.7%)

Memory
-14.0MiB live, 583.0MiB allocated
Rules
17 708×lower-fma.f64
17 708×lower-fma.f32
16 678×lower-fma.f64
16 678×lower-fma.f32
15 972×lower-fma.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04766142
115295822
238425766
084105318
04526425
114376180
237555990
084295450
0616
01016
15316
238016
3476616
0821016
0107496
1314496
2775489
32829489
46198489
08141458
03833943
111723693
232753605
379463605
082053345
Stop Event
fuel
iter limit
node limit
iter limit
node limit
iter limit
node limit
iter limit
iter limit
node limit
iter limit
node limit
Compiler

Compiled 300 to 220 computations (26.7% saved)

preprocess133.0ms (1.1%)

Memory
28.3MiB live, 152.2MiB allocated
Compiler

Compiled 316 to 166 computations (47.5% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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